Katsuhisa MIMACHI

Updated on: March, 2001

[To Center for Hypergeometric Systems/WWW]

Recent 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 ]

2. Mimachi, K.: A duality of the Macdonald-Koornwinder polynomials and its application to the integral representations, preprint 1999.

Recent Publications (1994 -)

1. Mimachi,K.: Holonomic q-difference system of the first order associated with a Jackson integral of Selberg type, Duke Math. J., 73 (1994), 453-468

2. Mimachi,K.: Macdonald's operator from the center of the quantized universal enveloping algebra $U_q(gl(N))$, International Mathematics Research Notices 10 (1994), 415-424

3. Mimachi,K.: One-point functions of the XXZ model and Ramanujan's $_1\Psi_1$ sum, J.Phys.A:Math.Gen. 27 (1994), 4157-4159

4. Mimachi,K. and Yamada,Yasuhiko: Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials, Commun.Math.Phys. 174 (1995) 447-455

5. Mimachi,K.: An integral representation of the solution of a fourth order Fuchsian differential equation of Okubo type, Funkt.Ekvac. 38 (1995), 411-416

6. Cho,K., Mimachi,K. and Yoshida,M.: A hypergeometric integral attached to the configration of the mirrors of the reflection group $S_{n+2}$ acting on $P_n$, Kyushu J.Math. 49 (1995), 11-34

7. Mimachi,K.: A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type, Duke Math. J. 85(1996), 635-658

8. Mimachi,K.and Noumi,M.: An integral representation of eigenfunctions for Macdonald's q-difference operators, Tohoku Math. J. 49(1997) 517-525.

9. Mimachi,K.and Noumi,M.: A reproducing kernel for nonsymmetric Macdonald polynomials, Duke Math. J. 91(1998) 621-634.

10. Mimachi,K.: The little q-Jacobi polynomial associated with a q-Selberg integral, Funkt. Ekvac. 41(1998) 91-100.

11. Mimachi,K.: A new derivation of the inner product formula for the Macdonald symmetric polynomials, Compositio Math. 113(1998), 117-122.

12. Mimachi,K.: A solution of the quantum Knizhnik Zamolodchikov equation of type $C_n$ , Commun. Math. Phys. 197(1998), 229-246.

13. Mimachi, K.: Eigenfunctions of Macdonald's $q$-difference operator for the root system of type $C_n$; J. Funct. Anal. 163(1999), 272--278.

14. Mimachi, K.: Barnes type integral and the Meixner-Pollaczek polynomials, Lett. Math. Phys. 48(1999), 365--373.

15. Mimachi, K.: A multidimensional generalization of the Barnes integral and the continuous Hahn polynomial, J. Math. Anal. and Appl. 234(1999), 67--76.

16. Mimachi, K.: Integral representations of the Wilson polynomials and the continuous dual Hahn polynomials, Adv. in Appl. Math. 23 (1999), 340--359.

17. Mimachi, K.: Askey-Wilson polynomials by means of a $q$-Selberg type integral, Adv. in Math. 147(1999), 315--327.