## Lie群論・表現論セミナー

開催情報 火曜日　16:30～18:00　数理科学研究科棟(駒場) 126号室 小林俊行 https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2009年10月15日(木)

16:30-18:00   数理科学研究科棟(駒場) 122号室

Hecke-Clifford superalgebras and crystals of type $D^{(2)}_{l}$
[ 講演概要 ]
It is known that we can sometimes describe the representation theory of Hecke algebra'' by Lie theory''. Famous examples that involve the Lie theory of type $A^{(1)}_n$ are Lascoux-Leclerc-Thibon's interpretation of Kleshchev's modular branching rule for the symmetric groups and Ariki's theorem generalizing Lascoux-Leclerc-Thibon's conjecture for the Iwahori-Hecke algebras of type A.

Brundan and Kleshchev showed that some parts of the representation theory of the affine Hecke-Clifford superalgebras and its finite-dimensional cyclotomic'' quotients are controlled by the Lie theory of type $A^{(2)}_{2l}$ when the quantum parameter $q$ is a primitive $(2l+1)$-th root of unity.
In this talk, we show that similar theorems hold when $q$ is a primitive $4l$-th root of unity by replacing the Lie theory of type $A^{(2)}_{2l}$ with that of type $D^{(2)}_{l}$.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html