Abstract:
Kostka polynomials are closely related to the representation theoryof finite general linear groups. In his study of character sheaves, Lusztig introduced some analogue of Kostka polynomials associated to therepresentation theory of finite reductive groups. In the case of classical groups, such functionscan be reconstructed in a combinatorial way as in the case of GL_n. By extending this, one can define Kostka functions associated to complex reflection groups . These are purely combinatorial objects, and no backbone from algebraic groups. However，recently an interesting relationship with representation theory of GL_n andSp_2n was found. In this talk, I will explain the construction of Kostkafunctions associated to complex reflection groups, and discuss their relationship with geometryinvolving those groups.