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三町勝久 研究業績一覧 (46件)
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論文
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K. Mimachi,
T.Takamuki.
A generalization of the Beta integral arising from the Knizhnik-Zamolodchikov equation for the vector representations of types Bn, Cn and D_n,
Kyushu J. Math.,
Vol. 59,
pp. 117--126,
2005.
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K. Mimachi.
Homological representations of the Iwahori-Hecke algebra associated with a Selberg type integral,
International Mathematics Research Notices,
Vol. 33,
pp. 2031--2057,
2005.
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K. Mimachi,
M.Yoshida.
Intersection numbers of twisted cycles associated with the Selberg integral and an application to the conformal field theory,
Commun. Math. Phys,
Vol. 250,
pp. 23--45,
2004.
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K. Mimachi,
K.Ohara,
M.Yoshida.
Intersection numbers for loaded cycles associated with Selberg integrals,
Tohoku Math. J .,
Vol. 56,
pp. 531--551,
2004.
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K. Mimachi,
M.Yoshida.
The reciplocity relation of the Selberg function,
J. Computational and Applied Math.,
Vol. 160,
pp. 209--215,
2003.
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K. Mimachi,
M.Yoshida.
Intersection numbers of twisted cycles and the correlation functions of the conformal field theory,
Commun. Math. Phys.,
Vol. 234,
pp. 265--281,
2003.
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K. Mimachi,
H. Ochiai,
M.Yoshida.
Intersection theory for loaded cycles IV -- resonant cases,
Math. Nachr.,
Vol. 260,
pp. 67--77,
2003.
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Katsuhisa Mimachi.
A duality of the Macdonald-Koornwinder polynomials and its application to the integral representations,
Duke Math. J.,
Vol. 107,
pp. 265-281,
2001.
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Katsuhisa Mimachi.
Askey-Wilson polynomials by means of a $q$-Selberg type integral,
Adv. in Math.,
Vol. 147,
pp. 315-327,
1999.
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Katsuhisa Mimachi.
Integral representations of the Wilson polynomials and the continuous dual Hahn polynomials,
Adv. in Appl. Math.,
Vol. 23,
pp. 340-359,
1999.
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Katsuhisa Mimachi.
A multidimensional generalization of the Barnes integral and the continuous Hahn polynomial,
J. Math. Anal. and Appl.,
Vol. 234,
pp. 67-76,
1999.
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Katsuhisa Mimachi.
Barnes type integral and the Meixner-Pollaczek polynomials,
Lett. Math. Phys.,
Vol. 48,
pp. 365-373,
1999.
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Katsuhisa Mimachi.
Eigenfunctions of Macdonald's $q$-difference operator for the root system of type $C_n\;$,
J. Funct. Anal.,
Vol. 163,
pp. 272-278,
1999.
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Katsuhisa Mimachi.
A reproducing kernel for nonsymmetric Macdonald polynomials,
Duke Math. J.,
Vol. 91,
pp. 621-634,
1998.
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Katsuhisa Mimachi.
The little $q$-Jacobi polynomial associated with a $q$-Selberg integral,
Funkt. Ekvac.,
Vol. 41,
pp. 91-100,
1998.
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Katsuhisa Mimachi.
A new derivation of the inner product formula for the Macdonald symmetric polynomials,
Composit. Math.,
Vol. 113,
pp. 117-122,
1998.
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Katsuhisa Mimachi.
A solution of the quantum Knizhnik Zamolodchikov equation of type $C_n\;$,
Commun. Math. Phys.,
Vol. 197,
pp. 229-246,
1998.
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Katsuhisa Mimachi.
An integral representation of eigenfunctions for Macdonald's $q$-difference operators,
Tohoku Math. J.,
Vol. 49,
pp. 517-525,
1997.
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Katsuhisa Mimachi.
A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of Macdonald type,
Duke Math. J.,
Vol. 85,
pp. 635-658,
1996.
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Katsuhisa Mimachi.
Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials,
Commun. Math. Phys.,
Vol. 174,
pp. 447-455,
1995.
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Katsuhisa Mimachi.
A hypergeometric integral attached to the configuration of the mirrors of the reflection group $S{n+2}$ acting on $Pn$,
Kyushu J. Math.,
Vol. 49,
pp. 11-34,
1995.
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Katsuhisa Mimachi.
An integral representation of the solution of a fourth order Fuchsian differential equation of Okubo type,
Funkt. Ekvac.,
Vol. 38,
pp. 411-416,
1995.
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Katsuhisa Mimachi.
Holonomic $q$-difference system of the first order associated with a Jackson integral of Selberg type,
Duke Math. J.,
Vol. 73,
pp. 453-468,
1994.
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Katsuhisa Mimachi.
One-point functions for the XXZ model and Ramanujan's $1\Psi1$ sum,
J. Phys. A: Math. Gen.,
Vol. 27,
pp. 4157-4159,
1994.
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Katsuhisa Mimachi.
Macdonald's operator from the center of the quantized universal enveloping algebra $U_q(gl(N))$,
International Mathematics Research Notices,
Vol. 10,
pp. 415-424,
1994.
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Katsuhisa Mimachi.
Holonomic $q$-difference system associated with the basic hypergeometric series ${n+1}\varphin\,$,
Tohoku Math. J.,
Vol. 45,
pp. 485-490,
1993.
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Katsuhisa Mimachi.
Finite dimensional representations of the quantum group $GLq(n;C)$ and the zonal spherical functions on $Uq(n-1)/U_q(n)$,
Japanese J. Math.,
Vol. 19,
pp. 31-80,
1993.
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Katsuhisa Mimachi.
Reducibility and irreducibility of the Gauss-Manin system associated with a Selberg type integral,
Nagoya Math. J.,
Vol. 132,
pp. 43-62,
1993.
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Katsuhisa Mimachi.
A solution of Yang-Baxter equation as connection coefficients of a holonomic $q$-difference system,
Duke Math. J.,
Vol. 65,
pp. 7-15,
1992.
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Katsuhisa Mimachi.
Spherical functions on a family of quantum 3-spheres,
Composit. Math.,
Vol. 83,
pp. 19-42,
1992.
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Katsuhisa Mimachi.
Askey-Wilson polynomials as spherical functions on SU_q(2),
Lecture Notes in Math.,
Vol. 1510,
pp. 98--103,
1992.
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Katsuhisa Mimachi.
Representation of the quantum group $SU_q(2)$ and the little $q$-Jacobi polynomials,
J. Funct. Anal.,
Vol. 99,
pp. 357-386,
1991.
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Katsuhisa Mimachi.
Rogers' $q$-ultraspherical polynomials on a quantum 2-sphere,
Duke Math. J.,
Vol. 63,
pp. 65-80,
1991.
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Katsuhisa Mimachi.
Unitary representations of the quantum group $SUq(1,1)$: Structure of the dual Space of $Uq(sl(2))$,
Lett. Math.Phys.,
Vol. 19,
pp. 187-194,
1990.
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Katsuhisa Mimachi.
Quantum 2-spheres and big $q$-Jacobi polynomials,
Commun. Math. Phys.,
Vol. 128,
pp. 521-531,
1990.
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Katsuhisa Mimachi.
Big $q$-Jacobi polynomials, $q$-Hahn polynomials and a family of quantum 3-spheres,
Lett. Math. Phys.,
Vol. 19,
pp. 299-305,
1990.
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Katsuhisa Mimachi.
Askey-Wilson polynomials and the quantum group $SU_q (2)$,
Proc. Japan Acad.,
Vol. 68,
pp. 146-149,
1990.
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T.Masuda,
K. Mimachi,
Y.Nakagami,
M.Noumi,
Y. Saburi,
K.Ueno.
Matrix elements of unitary representations of the quantum group $SU_q(1,1)$ and the basic hypergeometric functions,
Differential geometric methods in theoretical physics,
pp. 331-343,
1990.
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Katsuhisa Mimachi.
Representation of quantum groups,
Progress in Math,
Vol. 84,
1990.
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Katsuhisa Mimachi.
Unitary representations of the quantum group $SU_q(1,1)$:II-Matrix elements of Unitary representations and the basic hypergeometric functions,
Lett. Math. Phys.,
Vol. 19,
pp. 195-204,
1990.
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Katsuhisa Mimachi.
Zonal spherical functions on the quantum homogeneous space $SUq(n+1)/SUq(n)$,
Proc. Japan Acad,
Vol. 65,
1989.
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Katsuhisa Mimachi.
Connection problem in holonomic $q$-difference system associated with a Jackson integral of Jordan-Pochhammer type,
Nagoya Math. J,
Vol. 116,
1989.
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Katsuhisa Mimachi.
Representations of the quantum groups and a q-analogue of orthogonal polynomials,
C.R. Acad. Sci. Paris,
Vol. 307,
1988.
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Katsuhisa Mimachi.
A proof of Ramanujan's identity by use of loop integrals,
SIAM J. Math. Anal.,
Vol. 19,
1988.
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