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Unipotent Hecke algebras for finite groups of Lie type
Algebra & Discrete Mathematics| Speaker: | Nat Thiem, University of Wisconsin, Madison |
| Location: | 693 Kerr |
| Start time: | Fri, Sep 26 2003, 2:10PM |
Description
This talk examines the structure and representation theory of unipotent
Hecke algebras. We construct them with the following ingredients: a
finite group of Lie type $G$ (such as the general linear group over a
finite field), a maximal unipotent subgroup $U$ of $G$ (such as the
subgroup of upper-triangular matrices with ones on the diagonal), and a
one-dimensional $U$-module $\psi$. The double cosets $U\backslash G/U$
determine a natural basis for unipotent Hecke algebras, whose
multiplication relations have a skein-like algorithm. In the case
$G=GL_n(F_q)$, the combinatorics of partitions and weighted column strict
tableaux governs the representation theory, giving rise to an explicit
combinatorial map from the natural basis to pairs of multi-tableaux (also
known as an RSK-insertion).