Jay Taylor (Kaiserslautern)

Decomposing Generalised Gelfand-Graev Representations

Abstract:

In 1986 Kawanaka introduced a family of characters (over a field of characteristic zero) called GGGRs for any finite reductive group $G$ defined over a field of good characteristic. A long standing problem has been to determine the decomposition of these characters into the ordinary irreducible characters of $G$. Kawanaka solved this problem when $G$ is $\GL_n(q)$ or an adjoint exceptional group. In 1992 Lusztig gave a decomposition of the GGGRs in terms of character sheaves, under some assumptions on the field defining $G$. In this talk we will survey a program to determine the decomposition of GGGRs for classical-type groups using Lusztig's result.