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The Irreducibility of the Monodromy Representation Associated with the Dotsenko–Fateev Equation
Katsuhisa Mimachi
Communications in Mathematical Physics Vol. 405 No. 3 2024/03/04 Research paper (scientific journal)
Publisher: Springer Science and Business Media LLC
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A simple proof of Slater’s transformations for bilateral series $${}_{r}\psi _{r},\, {}_{2r}\psi _{2r}$$ and $${}_{2r-1}\psi _{2r-1}$$
Katsuhisa Mimachi
The Ramanujan Journal Vol. 64 No. 1 p. 67-78 2024/01/03 Research paper (scientific journal)
Publisher: Springer Science and Business Media LLC
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Yet another proof of Ramanujan's ${}_1\psi_1$ sum
Katsuhisa Mimachi
Proc. Amer. Math. Soc. Vol. 151 p. 3503-3512 2023
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Connection formulas related with Appell's hypergeometric function $F_1$
Katsuhisa Mimachi
PoS MA2019 (2022) 010 p. 1-73 2022/02 Research paper (international conference proceedings)
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Connection formulas related with Appell's $F_2$, Horn's $H_2$ and Olsson's $F_P$ functions
Katsuhisa Mimachi
Kyushu Journal of Mathematics Vol. 74 No. 1 p. 15-42 2020/02 Research paper (scientific journal)
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Integral representations of Appell's $F_2, F_3$, Horn's $H_2$ and Olsson's $F_P$ functions
Katsuhisa Mimachi
Kyushu Journal of Mathematics Vol. 74 No. 1 p. 1-13 2020/02 Research paper (scientific journal)
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Complex hypergeometric integrals
Katsuhisa Mimachi
Advanced Studies in Pure Mathematics Vol. 76 p. 469-486 2018 Research paper (scientific journal)
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Nakagiri's monodromy representations associated with Appell's hypergeometric functions $F_2$ and $F_3$
Katsuhisa Mimachi
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA Vol. 60 No. 1 p. 77-132 2017/04 Research paper (scientific journal)
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On a fundamental set of solutions to the generalized hypergeometric equation ${}_{n+1}E_{n}$ represented by integrals of Euler type
Katsuhisa Mimachi
KYUSHU JOURNAL OF MATHEMATICS Vol. 70 No. 2 p. 375-399 2016/09 Research paper (scientific journal)
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Solutions in terms of integrals of multivalued functions for the classical hypergeometric equations and the hypergeometric system on the configuration space
Katsuhisa Mimachi, Masatoshi Noumi
KYUSHU JOURNAL OF MATHEMATICS Vol. 70 No. 2 p. 315-342 2016/09 Research paper (scientific journal)
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The hypergeometric systems and the contiguity operators on the Grassmannian manifold and on the associated configuration space
Katsuhisa Mimachi, Takeshi Sasaki
INTERNATIONAL JOURNAL OF MATHEMATICS Vol. 27 No. 6 2016/06 Research paper (scientific journal)
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Monodromy representations associated with the generalized hypergeometric function ${}_{n+1}F_{n}$ and their reducibility
Katsuhisa Mimachi
KYUSHU JOURNAL OF MATHEMATICS Vol. 70 No. 1 p. 105-129 2016/03 Research paper (scientific journal)
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Reducibility of the systems of differential equations satisfied by Appell's $F_2, F_3$ and $F_4$
Katsuhisa Mimachi, Takeshi Sasaki
KYUSHU JOURNAL OF MATHEMATICS Vol. 69 No. 2 p. 429-435 2015/09 Research paper (scientific journal)
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The connection problem associated with a Selberg type integral and the $q$-Racah polynomials
Katsuhisa Mimachi
FORUM MATHEMATICUM Vol. 25 No. 6 p. 1127-1179 2013/11 Research paper (scientific journal)
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Monodromy representations associated with the Gauss hypergeometric function using integrals of a multivalued function
Katsuhisa Mimachi, Takeshi Sasaki
KYUSHU JOURNAL OF MATHEMATICS Vol. 66 No. 1 p. 35-60 2012/03 Research paper (scientific journal)
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Irreducibility and reducibility of Lauricella's system of differential equations $E_D$ and the Jordan-Pochhammer differential equation $E_{JP}$
Katsuhisa Mimachi, Takeshi Sasaki
KYUSHU JOURNAL OF MATHEMATICS Vol. 66 No. 1 p. 61-87 2012/03 Research paper (scientific journal)
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Monodromy representations associated with Appell's hypergeometric function $F_1$ using integrals of a multivalued function
Katsuhisa Mimachi, Takeshi Sasaki
KYUSHU JOURNAL OF MATHEMATICS Vol. 66 No. 1 p. 89-114 2012/03 Research paper (scientific journal)
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Solutions for some families of Fuchsian differential equations free from accessory parameters in terms of the integral of Euler type
Katsuhisa Mimachi
ARRANGEMENTS OF HYPERPLANES - SAPPORO 2009 Vol. 62 p. 233-260 2012 Research paper (international conference proceedings)
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A connection problem for Simposon's even family of rank four
Yoshishige Haraoka, Katsuhisa Mimachi
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA Vol. 54 No. 3 p. 495-515 2011/12 Research paper (scientific journal)
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The Jones polynomial and the intersection numbers of twisted cycles associated with a Selberg type integral
Katsuhisa Mimachi
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS Vol. 20 No. 3 p. 469-496 2011/03 Research paper (scientific journal)
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Intersection numbers for twisted cycles and the connection problem associated with the generalized hypergeometric function ${}_{n+1}F_{n}$
Katsuhisa Mimachi
INTERNATIONAL MATHEMATICS RESEARCH NOTICES Vol. 2011 No. 8 p. 1757-1781 2011 Research paper (scientific journal)
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Connection matrices associated with the generalized hypergeometric function ${}_3F_2$
Katsuhisa Mimachi
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA Vol. 51 No. 1 p. 107-133 2008/04 Research paper (scientific journal)
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Regularizable cycles associated with a Selberg type integral under some resonance condition
Katsuhisa Mimachi, Masaaki Yoshida
INTERNATIONAL JOURNAL OF MATHEMATICS Vol. 18 No. 4 p. 395-409 2007/04 Research paper (scientific journal)
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Jackson's integral of the Hurwitz zeta function
Nobushige Kurokawa, Katsuhisa Mimachi, Masato Wakayama
Rendiconti del Circolo Matematico di Palermo Vol. 56 No. 1 p. 43-56 2007/02 Research paper (scientific journal)
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Homological representations of the Iwahori-Hecke algebra associated with a Selberg-type integral
Katsuhisa Mimachi
INTERNATIONAL MATHEMATICS RESEARCH NOTICES Vol. 33 No. 33 p. 2031-2057 2005/07 Research paper (scientific journal)
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A generalization of the Beta integral arising from the Knizhnik-Zamolodchikov equation for the vector representations of type $B_{n},\, C_{n}$ and $D_n$
Katsuhisa Mimachi, Takashi Takamuki
KYUSHU JOURNAL OF MATHEMATICS Vol. 59 No. 1 p. 117-126 2005/03 Research paper (scientific journal)
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Intersection numbers for loaded cycles associated with Selberg-type integrals
Katsuhisa Mimachi, Katsuyoshi Ohara, Masaaki Yoshida
TOHOKU MATHEMATICAL JOURNAL Vol. 56 No. 4 p. 531-551 2004/12 Research paper (scientific journal)
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Intersection numbers of twisted cycles associated with the Selberg integral and an application to the conformal field theory
Katsuhisa Mimachi, Masaaki Yoshida
COMMUNICATIONS IN MATHEMATICAL PHYSICS Vol. 250 No. 1 p. 23-45 2004/09 Research paper (scientific journal)
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The reciprocity relation of the Selberg function
Katsuhisa Mimachi, Masaaki Yoshida
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Vol. 160 No. 1-2 p. 209-215 2003/11 Research paper (scientific journal)
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Intersection numbers of twisted cycles and the correlation functions of the conformal field theory
Katsuhisa Mimachi, Masaaki Yoshida
COMMUNICATIONS IN MATHEMATICAL PHYSICS Vol. 234 No. 2 p. 339-358 2003/03 Research paper (scientific journal)
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Intersection theory for loaded cycles IV - resonant cases
Katsuhisa Mimachi, Hiroyuki Ochiai, Masaaki Yoshida
MATHEMATISCHE NACHRICHTEN Vol. 260 p. 67-77 2003 Research paper (scientific journal)
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A duality of Macdonald-Koornwinder polynomials and its application to integral representations
Katsuhisa Mimachi
DUKE MATHEMATICAL JOURNAL Vol. 107 No. 2 p. 265-281 2001/04 Research paper (scientific journal)
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Integral representations of the Wilson polynomials and the continuous dual Hahn polynomials
Katsuhisa Mimachi
ADVANCES IN APPLIED MATHEMATICS Vol. 23 No. 4 p. 340-359 1999/11 Research paper (scientific journal)
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Askey-Wilson polynomials by means of a $q$-Selberg type integral
Katsuhisa Mimachi
ADVANCES IN MATHEMATICS Vol. 147 No. 2 p. 315-327 1999/11 Research paper (scientific journal)
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Barnes-type integral and the Meixner-Pollaczek polynomials
Katsuhisa Mimachi
LETTERS IN MATHEMATICAL PHYSICS Vol. 48 No. 4 p. 365-373 1999/06 Research paper (scientific journal)
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A multidimensional generalization of the Barnes integral and the continuous Hahn polynomial
Katsuhisa Mimachi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Vol. 234 No. 1 p. 67-76 1999/06 Research paper (scientific journal)
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Eigenfunctions of Macdonald's $q$-difference operator for the root system of type $C_{n}$
Katsuhisa Mimachi
JOURNAL OF FUNCTIONAL ANALYSIS Vol. 163 No. 2 p. 272-278 1999/04 Research paper (scientific journal)
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A new derivation of the inner product formula for the Macdonald symmetric polynomials
Katsuhisa Mimachi
COMPOSITIO MATHEMATICA Vol. 113 No. 2 p. 117-122 1998/09 Research paper (scientific journal)
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A solution of the quantum Knizhnik Zamolodchikov equation of type $C_n$
Katsuhisa Mimachi
COMMUNICATIONS IN MATHEMATICAL PHYSICS Vol. 197 No. 1 p. 229-246 1998/09 Research paper (scientific journal)
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A reproducing kernel for nonsymmetric Macdonald polynomials
Katsuhisa Mimachi, Masatoshi Noumi
DUKE MATHEMATICAL JOURNAL Vol. 91 No. 3 p. 621-634 1998/02 Research paper (scientific journal)
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The little $q$-Jacobi polynomial associated with a $q$-Selberg integral
Katsuhisa Mimachi
Funkt. Ekvac. Vol. 41 p. 91-100 1998 Research paper (scientific journal)
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An integral representation of eigenfunctions for Macdonald’s $q$-difference operators
Katsuhisa Mimachi, Masatoshi Noumi
Tohoku Mathematical Journal Vol. 49 No. 4 p. 517-525 1997/01/01 Research paper (scientific journal)
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A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type
Katsuhisa Mimachi
Duke Mathematical Journal Vol. 85 No. 3 p. 635-658 1996/12 Research paper (scientific journal)
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Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials
Katsuhisa Mimachi, Yasuhiko Yamada
Communications in Mathematical Physics Vol. 174 No. 2 p. 447-455 1995/12 Research paper (scientific journal)
Publisher: Springer-Verlag
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An integral representation of the solution of a fourth order Fuchsian differential equation of Okubo type
Katsuhisa Mimachi
Funkt. Ekvac. Vol. 38 p. 411-416 1995/06 Research paper (scientific journal)
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A hypergeometric integral attached to the configuration of the mirrors of the reflection group $S_{n+2}$ acting on $\mathbb{P}_n$
Koji Cho, Katsuhisa Mimachi, Masaaki Yoshida
Kyushu Journal of Mathematics Vol. 49 No. 1 p. 11-34 1995 Research paper (scientific journal)
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One-point functions for the XXZ model and Ramanujan's ${}_1\Psi_1$
Katsuhisa Mimachi
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL Vol. 27 No. 12 p. 4157-4159 1994/06 Research paper (scientific journal)
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Holonomic $q$-difference system of the first order associated with a Jackson integral of Selberg type
Katsuhisa Mimachi
Duke Mathematical Journal Vol. 73 No. 2 p. 453-468 1994 Research paper (scientific journal)
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Macdonald's operator from the center of the quantized universal enveloping algebra $U_q(\,g\ell\,(N)\,)$
Katsuhisa Mimachi
International Mathematics Research Notices Vol. 1994 No. 10 p. 415-424 1994 Research paper (scientific journal)
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Finite dimensional representations of the quantum group GL_q(n;C) and the zonal spherical functions on U_q(n-1)\U_q(n)
NOUMI Masatoshi, YAMADA Hirofumi, MIMACHI Katsuhisa
Japanese journal of mathematics. New series Vol. 19 No. 1 p. 31-80 1993/06 Research paper (scientific journal)
Publisher: The Mathematical Society of Japan
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Holonomic $q$-difference system associated with the basic hypergeometric series ${}_{n+1} \varphi_{n}$
Katsuhisa Mimachi
Tohoku Mathematical Journal Vol. 45 No. 4 p. 485-490 1993 Research paper (scientific journal)
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Reductibility and irreducibility of the Gauss-Manin system associated with a Selberg type integral
Katsuhisa Mimachi
Nagoya Mathematical Journal Vol. 132 p. 43-62 1993 Research paper (scientific journal)
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Spherical functions on a family of quantum $3$-spheres
Msatoshi Noumi, Katsuhisa Mimachi
Composit. Math. Vol. 83 p. 19-42 1992/06 Research paper (scientific journal)
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Askey-Wilson polynomials as spherical functions on $SU_q(2)$
Masatoshi Noumi, Katsuhisa Mimachi
LECTURE NOTES IN MATHEMATICS Vol. 1510 p. 97-103 1992 Research paper (scientific journal)
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A solution of the Yang-Baxter equation as connection coefficients of a holonomic $q$-difference system
Kazuhiko Aomoto, Yoshifumi Kato, Katsuhisa Mimachi
International Mathematics Research Notices Vol. 1992 No. 1 p. 7-15 1992 Research paper (scientific journal)
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Representations of the quantum group SU_q(2) and the little q-Jacobi polynomials
MASUDA T.
J. Functional Analysis Vol. 99 p. 357-386 1991/06 Research paper (scientific journal)
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Rogers' $q$-ultraspherical polynomials on a quantum $2$-sphere
Masatoshi Noumi, Katsuhisa Mimachi
DUKE MATHEMATICAL JOURNAL Vol. 63 No. 1 p. 65-80 1991/06 Research paper (scientific journal)
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Askey-Wilson polynomials and the quantum group $SU_q (2)$
Masatoshi Noumi, Katsuhisa Mimachi
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES Vol. 66 No. 6 p. 146-149 1990/06 Research paper (scientific journal)
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Big $q$-Jacobi polynomials, $q$-Hahn polynomials and a family of quantum $3$-spheres
Masatoshi Noumi, Katsuhisa Mimachi
Letters in Mathematical Physics Vol. 19 No. 4 p. 299-305 1990/05 Research paper (scientific journal)
Publisher: Kluwer Academic Publishers
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Unitary representations of the quantum group $SU_q(1,1)$: Structure of the dual Space of $U_q(s\ell\,(2))$
Tetsuya Masuda, Katsuhisa Mimachi, Yoshiomi Nakagami, Masatoshi Noumi, Yutaka Saburi, Kimio Ueno
Letters in Mathematical Physics Vol. 19 No. 3 p. 187-194 1990/04 Research paper (scientific journal)
Publisher: Kluwer Academic Publishers
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Unitary representations of the quantum group $SU_q(1,1)$:II-Matrix elements of Unitary representations and the basic hypergeometric functions
Tetsuya Masuda, Katsuhisa Mimachi, Yoshiomi Nakagami, Masatoshi Noumi, Yutaka Saburi, Kimio Ueno
Letters in Mathematical Physics Vol. 19 No. 3 p. 195-204 1990/04 Research paper (scientific journal)
Publisher: Kluwer Academic Publishers
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Representation of quantum groups
Tetsuya Masuda, Katsuhisa Mimachi, Yoshiomi Nakagami, Masatoshi Noumi, Kimio Ueno
Progress in Math., Vol. 84 p. 119-128 1990/03 Research paper (scientific journal)
Publisher: Birkh\"{a}user
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Matrix elements of Unitary representations of the quantum group $SU_q(1,1)$ and the basic hypergeometric functions
Kimio Ueno, Tetsuya Masuda, Katsuhisa Mimachi, Yoshiomi Nakagami, Masatoshi Noumi, Yutaka Saburi
DIFFERENTIAL GEOMETRIC METHODS IN THEORETICAL PHYSICS Vol. 245 p. 331-343 1990 Research paper (international conference proceedings)
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Quantum $2$-spheres and big $q$-Jacobi polynomials
Masatoshi Noumi, Katsuhisa Mimachi
COMMUNICATIONS IN MATHEMATICAL PHYSICS Vol. 128 No. 3 p. 521-531 1990 Research paper (scientific journal)
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Zonal spherical functions on the quantum homogeneous space $SU_q(n+1)/SU_q(n)$
Masatoshi Noumi, Hirofumi Yamada, Katsuhisa Mimachi
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES Vol. 65 No. 6 p. 169-171 1989/06 Research paper (scientific journal)
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Connection problem in holonomic $q$-difference system associated with a Jackson integral of Jordan-Pochhammer type
Katsuhisa Mimachi
Nagoya Mathematical Journal Vol. 116 p. 149-161 1989 Research paper (scientific journal)
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A proof of Ramanujan's identity by use of loop integrals
Katsuhisa Mimachi
SIAM J. Math. Anal. Vol. 19 p. 1490-1493 1988/06 Research paper (scientific journal)
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Representations of quantum groups and a q-analogue of orthogonal polynomials
MASUDA T.
C. R. Acad. Sci. Paris Vol. 307 p. 559-564 1988/06 Research paper (scientific journal)
