庄司 俊明 (名大多元数理)
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 $G(r,1,n)$.