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.

Lecture #12715

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Supplements

Right click on the link and "Save As..." to save to your local computer.

• 12715.pdf (1.5 MB)

Left click on thumbnail to see a larger image.

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 12715-12715-QuickTime.mov (403 MB)

See more of our Streaming Videos on our main VMath - Streaming Video page.