庄司 俊明 (名大多元数理)
タイトル:
Green functions associated to complex reflection groups
アブストラクト
Kostka polynomials, which have a close connection
with Green polynomials of finite general linear groups
$GL_n(F_q)$, are defined as the transition matrix
between Schur functions and Hall-Littlewood functions.
The notion of Green polynomials are generalized, by a
geometric method, to other classical
groups, such as $Sp_{2n}(F_q)$ or $SO_{2n+1}(F_q)$.
They are characterized by the corresponding Weyl groups
and some additiona data.
The complex reflection group $G(e,1,n)$ is a generalization
of the symmetric group $S_n$, and of the Weyl group of
type $B_n$. We construct Schur functions and Hall-Littlewood
functions associated to $G(e,1,n)$ generalizing the case
of type $A$, and define Kostka functions as a transition
matrix between them. As a special case, this gives a
combinatorial approach for Green polynomials of type
$B_n$ or $C_n$.