Katsuhisa MIMACHI

Department of Mathematics, Graduate School of Science and Engineering, Tokyo Institute of Technology
2-12-1 Oh-Okayama, Meguro-Ku, Tokyo, 152-8551, Japan

Updated on: June 18th, 2008.

[To Center for Hypergeometric Systems/WWW]


Preprints

  1. Mimachi,K. and Noumi,M.: Representations of the Hecke algebra on a family of rational functions (preprint, January 1997)
    [ AMSLaTeX, 9 pages : src / dvi / ps ]


Publications

  1. K. Mimachi, A proof of Ramanujan's identity by use of loop integrals, SIAM J. Math. Anal., 19(1988), 1490--1493.
  2. T.Masuda, K.Mimachi, Y.Nakagami, M.Noumi, K.Ueno, Representations of the quantum groups and a q-analogue of orthogonal polynomials, C.R. Acad. Sci. Paris, Ser. I Math., 307 (1988), 559--564.
  3. K. Mimachi, Connection problem in holonomic q-difference system associated with a Jackson integral of Jordan-Pochhammer type, Nagoya Math. J., 116 (1989), 149--161.
  4. M.Noumi, H.Yamada and K. Mimachi, Zonal spherical functions on the quantum homogeneous space SUq(n+1)/SUq(n), Proc. Japan Acad., 65 (1989) , 169--171.
  5. T.Masuda, K. Mimachi, Y.Nakagami, M.Noumi, K.Ueno, Representation of quantum groups, in ``Mappings of operator algebras (H.Araki and R.Kadison eds.)": Progress in Math., 84 (1990), pp.119--128, Birkh\"{a}user.
  6. T.Masuda, K. Mimachi, Y.Nakagami, M.Noumi, Y. Saburi, K.Ueno, Unitary representations of the quantum group SUq(1,1): Structure of the dual Space of Uq(sl(2)) , Lett. Math. Phys., 19 (1990), 187--194.
  7. T.Masuda, K. Mimachi, Y.Nakagami, M.Noumi, Y. Saburi, K.Ueno, Unitary representations of the quantum group SUq(1,1) II :-Matrix elements of Unitary representations and the basic hypergeometric functions, Lett. Math. Phys., 19 (1990), 195--204.
  8. M.Noumi and K. Mimachi, Quantum 2-spheres and big q-Jacobi polynomials, Commun. Math. Phys., 128 (1990), 521--531.
  9. M.Noumi and K. Mimachi, Big q-Jacobi polynomials, q-Hahn polynomials and a family of quantum 3-spheres , Lett. Math. Phys.,19 (1990), 299--305.
  10. M. Noumi and K. Mimachi, Askey-Wilson polynomials and the quantum group SUq (2) , Proc. Japan Acad., 68 (1990), 146--49.
  11. T.Masuda, K. Mimachi, Y.Nakagami, M.Noumi, Y. Saburi, K.Ueno, Matrix elements of unitary representations of the quantum group SUq(1,1) and the basic hypergeometric functions, in ``Differential geometric methods in theoretical physics (Davis, CA, 1988)" ( Chau L.-L. ed.), pp.331--343, Plenum, New York 1990. NATO Adv. Sci. Inst. Ser.B, Phys.,245.
  12. T.Masuda, K. Mimachi, Y.Nakagami, M.Noumi, K.Ueno, K. Mimachi,Representation of the quantum group SUq(2) and the little q-Jacobi polynomials, J. Funct. Anal., 99 (1991), 357--386.
  13. M. Noumi and K. Mimachi, Rogers' q-ultraspherical polynomials on a quantum 2-sphere, Duke Math. J., 63 (1991), 65--80.
  14. M. Noumi and K. Mimachi, Spherical functions on a family of quantum 3-spheres, Composit. Math., 83 (1992), 19--42.
  15. M. Noumi and K. Mimachi, Askey-Wilson polynomials as spherical functions on SUq(2), in ``Quantum Groups "(P.P.Kulish ed.) : Lecture Notes in Math., 1510, pp.98--103, Springer 1992.
  16. K.Aomoto, Y.Kato and K. Mimachi, @A solution of Yang-Baxter equation as connection coefficients of a holonomic q-difference system, Duke Math. J., 65(1992), International Mathematics Research Notices 7--15.
  17. M.Noumi, H.Yamada and K. Mimachi, Finite dimensional representations of the quantum group GLq(n;C) and the zonal spherical functions on Uq(n-1)/Uq(n) , Japanese J. Math., 19 (1993), 31--80.
  18. K. Mimachi, Holonomic q-difference system associated with the basic hypergeometric series n+1\varphi n, Tohoku Math. J., 45(1993), 485--490.
  19. K. Mimachi, Reducibility and irreducibility of the Gauss-Manin system associated with a Selberg type integral, Nagoya Math. J., 132(1993), 43--62.
  20. K. Mimachi, Holonomic q-difference system of the first order associated with a Jackson integral of Selberg type, Duke Math. J., 73 (1994), 453--468.
  21. K. Mimachi, One-point functions for the XXZ model and Ramanujan's 1\Psi1 sum, J. Phys. A: Math. Gen., 27 (1994), 4157--4159.
  22. K. Mimachi, Macdonald's operator from the center of the quantized universal enveloping algebra Uq(gl(N)), International Mathematics Research Notices, 10 (1994), 415--424.
  23. K. Mimachi, An integral representation of the solution of a fourth order Fuchsian differential equation of Okubo type, Funkt. Ekvac., 38 (1995), 411--416.
  24. K.Cho, K. Mimachi and M.Yoshida, A hypergeometric integral attached to the configuration of the mirrors of the reflection group Sn+2 acting on Pn, Kyushu J. Math.,49 (1995), 11--34.
  25. K. Mimachi and Y.Yamada, Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials, Commun. Math. Phys., 174 (1995), 447--455.
  26. K. Mimachi, A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of Macdonald type, Duke Math. J., 85 (1996), 635--658.
  27. K. Mimachi and M.Noumi, An integral representation of eigenfunctions for Macdonald's q-difference operators, Tohoku Math. J., 49 (1997), 517--525.
  28. K. Mimachi and M. Noumi, A reproducing kernel for nonsymmetric Macdonald polynomials, Duke Math. J.,91 (1998), 621--634.
  29. K. Mimachi, The little q-Jacobi polynomial associated with a q-Selberg integral, Funkt. Ekvac., 41 (1998), 91--100.
  30. K. Mimachi, A new derivation of the inner product formula for the Macdonald symmetric polynomials, Composit. Math., 113(1998), 117--122.
  31. K. Mimachi, A solution of the quantum Knizhnik Zamolodchikov equation of type Cn, Commun. Math. Phys., 197(1998), 229--246.
  32. K. Mimachi, Eigenfunctions of Macdonald's q-difference operator for the root system of type Cn, J. Funct. Anal., 163 (1999), 272--278.
  33. K. Mimachi, Barnes type integral and the Meixner-Pollaczek polynomials, Lett. Math. Phys., 48 (1999), 365--373.
  34. K. Mimachi, A multidimensional generalization of the Barnes integral and the continuous Hahn polynomial, J. Math. Anal. and Appl., 234(1999), 67--76.
  35. K. Mimachi, Integral representations of the Wilson polynomials and the continuous dual Hahn polynomials, Adv. in Appl. Math., 23(1999), 340--359.
  36. K. Mimachi, Askey-Wilson polynomials by means of a q-Selberg type integral, Adv. in Math., 147 (1999), 315--327.
  37. K. Mimachi, A duality of the Macdonald-Koornwinder polynomials and its application to the integral representations, Duke Math. J., 107 (2001), 265--281.
  38. K. Mimachi and M.Yoshida, Intersection numbers of twisted cycles and the correlation functions of the conformal field theory, Commun. Math. Phys., 234 (2003), 339 --358.
  39. K. Mimachi, H. Ochiai and M.Yoshida, Intersection theory for loaded cycles IV -- resonant cases, Math. Nachr. 260 (2003), 67--77 .
  40. K. Mimachi and M.Yoshida, The reciplocity relation of the Selberg function, J. Computational and Applied Math. 160 (2003), 209--215.
  41. K. Mimachi, K.Ohara and M.Yoshida, Intersection numbers for loaded cycles associated with Selberg integrals, Tohoku Math. J . Tohoku Math. J . 56 (2004), 531--551.
  42. K. Mimachi and M.Yoshida, Intersection numbers of twisted cycles associated with the Selberg integral and an application to the conformal field theory, Commun. Math. Phys. 250 (2004), 23--45 .
  43. K. Mimachi and T.Takamuki, A generalization of the Beta integral arising from the Knizhnik-Zamolodchikov equation for the vector representations of types B_n, C_n and D_n, Kyushu J. Math. 59 (2005), 117--126.
  44. K. Mimachi, Homological representations of the Iwahori-Hecke algebra associated with a Selberg type integral, International Mathematics Research Notices. 33 (2005), 2031--2057.
  45. K. Mimachi and Masaaki Yoshida, Regularizable cycles associated with a Selberg-type integral under some resonance condition, Internat. Jour. Math. 18 (2007), 395--409.
  46. K. Mimachi, Connection matrices associated with the generalized hypergeometric function _3F_2, Funkt. Ekvac. 51 (2008), 107--133.

mimachi@math.titech.ac.jp