京都大学大学院 情報学研究科 数理工学専攻 応用数学講座 数理解析分野
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関西可積分系セミナー (2000年5月31日)

日時
2000年5月31日(水)15時-16時30分
場所
大阪大学基礎工学研究科数理科学ディスプレイ室(J617)
Alexander Orlov (京都大学理学部数学科)
Fermionic representation for basic hypergeometric functions related to Schur polynomials

We shall present a set of fermionic representations for the q-deformed hypergeometric functions related to Schur polynomials. We shall show that multivariate hypergeometric functions are tau-functions of the KP, TL hierarchies and their multicomponent counterparts. The variables of the hypergeometric functions are the higher times of those hierarchies. The discrete Toda lattice variables shifts parameters of hypergeometric functions. The role of additional symmetries and of Miwa change of variables with complex multiplicities will be explained. (joint work with D.M. Scherbin)