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 : 
 M.Noumi: Painlevé equations through symmetry, Translations of Mathematical Monographs Vol. 223, American Mathematical Society, 2004.
 M.Noumi and Y.Yamada: Tropical RobinsonSchenstedKnuth correspondence and birational Weyl group actions, Advanced Studies in Pure Mathematics 40(2004), Representation Theory of Algebraic Groups and Quanatum Groups, 371442 (mathph/0203030).
 K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Hypergeometric solutions to the $q$Painlevé equations, IMRN 2004, no.47, 24972521.
 M.Noumi and J.V.Stokman: AskeyWilson polynomials: an affine Hecke algebra approach, in Laredo Lectures on Orthogonal Polynomials and Special Functions(R.AlvarezNodarse, F.Marcellan and W.Van Assche, Eds), pp. 111144, Nova Science Publishers, 2004. (math.QA/0001033)
 K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Cremona transformations and the elliptic difference Painlevé equation (in Japanese), RIMS Kokyuroku 1400(2004), 197263.
 M.Noumi and Y.Yamada: Symmetries in Painlevé equations, Sugaku Expositions 17(2004), 203218. (Translation of Sugaku 53(2001), 6275, translated by T.Masuda)
 K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Cubic pencils and Painlevé Hamiltonians, Funkcial. Ekvac. 48(2005), 147160 (nlin.SI/0403009)
 K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Hypergeometric solutions to the $q$Painlevé equations (in Japanese), RIMS Kokyuroku 1422(2005), 7798.
 K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: Construction of hypergeometric solutions to the $q$Painlevé equations, IMRN 2005, no.24 14411463 (nlin.SI/0501051)


