[geometry-ml:02036] Seminar on Geometric representation theory and Quantum integrable system at Komaba

[Iwao Shinsuke]

 皆さま
（複数のMLに投稿しております。重複して受信された方は申し訳ありません。）

下記の日程にてセミナーをおこないますので、ご案内申し上げます。
 皆さまのご参加をお待ちしております。

世話人: 岩尾慎介（青山学院大） 白石潤一（東大・数理） 土屋昭博（IPMU） 山田裕二（立教大）

セミナーURL : https://sites.google.com/site/seminaratkomaba/home

岩尾慎介
青山学院理工
iwao ＠ gem.aoyama.ac.jp
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講演者：山根宏之氏　（富山大学数学教室）
日時：2014年5月10日（土）14:00～17:00
場所：東京大学大学院数理科学研究科   002号室
講演題目：Harish-Chandra-type theorem of generalized quantum groups

Abstract: Generalized quantum groups (GQGs for short) are a class of
Hopf algberas.
Their examples include: (a) the quantum groups, (b) the Lusztig's small
quantum groups at roots of unity
(our setting is that their Cartan parts are free),
(c) the multi-parameter quantum groups,
(d) the quantum groups associated with the basic classical Lie superalgebras,
and (e) the Drinfeld quantum doubles of the Nichols algebras of diagonal type.
The algebras in (e) was classified by Heckenberger (2009).
Let $U$ be a GQG whose root system $R$ is a finite set.
Symmetry of $R$ is depicted by its Weyl groupoid $W$.  Systematic study
of $W$ was undertaken by Heckenberger and the speaker (2008),
e.g., $W$ allows a Matsumoto-type theorem for the reduced expressions
of its elements.
They also gave a factorization formula of the Shapovalov determinants
of $U$ (it was new even for (b)) (2010), for which a key fact is that
$W$ acts on Verma modules $M$ of $U$
in the cases of roots of unity,
so that one gets explicitly singular vectors of $M$
corresponding to Shapovalov factors.
Using that formula, we establish a Harish-Chandra-type theorem
describing the center of $U$ in a Kac's algebraic-geometrical way
(this seems new even for (b)).
This is a joint work with Punita Batra, see arXiv:1309.1651.