タイトル： Green functions associated to complex reflection groups (2)

アブストラクト

This talk is a contimuation of the previous talk. In the previous talk, we have discussed the classical case, i.e, the combinatorics assciated to partitions, or $GL_n(F_q)$. In this talk, we introduce a combinatorics describing the unipotent classes in $Sp_{2n}(F_q)$ or $SO_{2n+1}(F_q)$, i.e., unipotent symbols. Unipotent symbols are a genralization of partitions. We construct Hall-Littlewood functions associated to unipotent symbols, and describe Green functions of $Sp_{2n}(F_q)$ in a combinatorial way, as in the case of $GL_n(F_q)$. This combinatorial scheme can be generalized to the situation where the Weyl group $W(B_n)$ is replaced by the complex reflection group $G(r,1,n)$.