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Homological Methods in Representation Theory |
| March 31, 2008 to April 04, 2008 |
| Organized By: David Benson, Daniel Nakano(chair), Raphael Rouquier |
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| Parent Programs: |
| Representation Theory of Finite Groups and Related Topics |
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| Return to Workshop Description |
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Tensoring with the Steinberg module
Thursday April 3, 2008
09:30AM - 10:30AM
Speakers:
Henning Andersen
Abstract:
Let $G$ be a semisimple algebraic group over a field of
characteristic $p > 0$ and denote by $U_q$ the corresponding quantum
group at a root of unity. In both cases we have a Steinberg module,
$St_p$ and $St_q$, respectively. This module is both simple, induced
from a Borel subgroup/subalgebra, and tilting.
We study the effect of tensoring finite dimensional modules for $G$
or $U_q$ by the Steinberg module. In particular, we prove that
if $L$ is a restricted module (for $G$ or $U_q$) then the
$L \otimes St_p$, respectively $L \otimes St_q$ is tilting.
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