関西可積分系セミナー (2005年5月20日)
- 日時
- 2005年5月20日（金）15時-16時30分
- 場所
- 京都大学本部キャンパス工学部総合校舎４０６セミナー室
津田照久 (神戸大学自然科学研究科)
Universal character and q-Painlevé equations
The universal character is a polynomial attached to a pair of partitions and is a generalization of the Schur polynomial. In this talk, we introduce an integrable system of q-difference lattice equations satisfied by the universal character; we call it the lattice q-UC hierarchy and regard it as generalizing both q-KP and q-UC hierarchies. Suitable similarity and periodic reductions of the hierarchy yield the q-Painlevé equations of types A2g+1, D5, and E6. As its consequence, a class of algebraic solutions of q-Painlevé equations is rapidly obtained by means of the universal character.