| 発表言語 |
日本語
|
| 開催日 |
2009年11月04日 10時30分
|
| 終了日 |
2009年11月04日 12時30分
|
| 開催場所 | 京都大学理学部3号館 (数学教室) 552号室 |
| セミナー名 | 表現論セミナー |
| タイトル |
Variations on a theme of Bezrukavnikov-Mirkovic-Rumynin |
| 分野 |
代数
幾何
解析
|
| 講演者名 | 谷崎 俊之 |
| 講演者所属 | 大阪市立大 |
| 概要 | Bezrukavnikov-Mirkovic-Rumynin gave a correspondence between
representations of simple Lie algebras in positive characteristics
and  -modules on the corresponding flag manifold.
The aim of the present talk is to give its analogue for quantized
enveloping algebras at roots of 1.
More precisely, we establish a derived equivalence between the
category of certain modules over the (De Concini-Kac type) quantized
enveloping algebras at roots of 1 and that of (crystalline) -modules on
the quantized flag manifold.
At roots of 1 we can associate a sheaf of rings  on the
ordinary flag manifold over the complex number field, so that the category
of -modules is equivalent to that of -modules.
Let  be the center of . We can show that is an
Azumaya algebra on  . We can also show that restrictions of
to certain closed subsets are split Azumaya algebras.
By those results we obtain a correspondence between representations of
quantized enveloping algebras at roots of 1 and  -modules on the
Springer fibers. This implies, for example, Lusztig's conjecture on the
number of
irreducible representations of quantized enveloping algebras with
specified central character.
A closely related result using a different definition of -modules
is also given by Backelin-Kremnizer. |
|