Masatoshi NOUMI

Masatoshi NOUMI

Department of Mathematics,
Graduate School of Science, Kobe University
Division : Analysis
Professor		 Building B, Room 212

Research Field : Algebraic analysis of integrable systems; Representation theory and Special functions
Research Summary : Main interests of my research are to study "good" functions defined by differential/difference equations, including hypergeometric functions and Painlevé transcendents in the broad sense, and to develop ideas of algebraic analysis and representation theory in linear and nonlinear integrable systems. Specifically: (1) Quantum symmetric spaces and their spherical functions (2) Lie theoretic approach to differential/difference equations of Painlevé type (3) Elliptic hypergeometric functions and elliptic integrable systems
Primary Publications :
  1. M.Noumi: Painlevé equations through symmetry, Translations of Mathematical Monographs Vol. 223, American Mathematical Society, 2004.
  2. M.Noumi and Y.Yamada: Tropical Robinson-Schensted-Knuth correspondence and birational Weyl group actions, Advanced Studies in Pure Mathematics 40(2004), Representation Theory of Algebraic Groups and Quanatum Groups, 371-442 (math-ph/0203030).
  3. K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Hypergeometric solutions to the $q$-Painlevé equations, IMRN 2004, no.47, 2497-2521.
  4. M.Noumi and J.V.Stokman: Askey-Wilson polynomials: an affine Hecke algebra approach, in Laredo Lectures on Orthogonal Polynomials and Special Functions(R.Alvarez-Nodarse, F.Marcellan and W.Van Assche, Eds), pp. 111-144, Nova Science Publishers, 2004. (math.QA/0001033)
  5. K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Cremona transformations and the elliptic difference Painlevé equation (in Japanese), RIMS Kokyuroku 1400(2004), 197-263.
  6. M.Noumi and Y.Yamada: Symmetries in Painlevé equations, Sugaku Expositions 17(2004), 203-218. (Translation of Sugaku 53(2001), 62-75, translated by T.Masuda)
  7. K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Cubic pencils and Painlevé Hamiltonians, Funkcial. Ekvac. 48(2005), 147-160 (nlin.SI/0403009)
  8. K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Hypergeometric solutions to the $q$-Painlevé equations (in Japanese), RIMS Kokyuroku 1422(2005), 77-98.
  9. K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Construction of hypergeometric solutions to the $q$-Painlevé equations, IMRN 2005, no.24 1441-1463 (nlin.SI/0501051)