| Date |
February 23 (Tue.) 18:00-19:30 |
| Speaker |
Jae-Hoon Kwon（Seoul National Univ.） |
| Title |
Classical crystals and combinatorial extension of stable branching rules |
| Place |
Osaka City University Academic Extension Center |
| Abstract |
We introduce a new combinatorial model of crystals associated to integrable highest weight modules over the classical Lie algebras of type B, C, D, called parabolically semistandard tableaux
(simply PSST). The notion of PSST, which also admits a natural super-analogue, has played a crucial role in proving the existence of crystal base of irreducible representations of ortho-symplectic Lie
superalgebras in a certain semisimple tensor category.
In this talk, as another application of PSST, we give combinatorial formulas for decomposition of the tensor product of integrable highest weight modules and branching decomposition of an integrable
highest weight module with respect to a maximal Levi subalgebra of type A. Then we show that our formulas naturally extend various stable branching rules for classical groups to arbitrary highest
weights, including the Littlewood's restriction rules.
|
| Date |
November 9 (Mon.) 18：00～19：30 |
| Speaker |
Liron Speyer（Osaka University） |
| Title |
Kleshchev's decomposition numbers for cyclotomic Hecke algebras |
| Place |
Osaka City University Academic Extension Center
|
| Abstract |
I will present recent joint work with Chris Bowman in which we calculate decomposition numbers for cyclotomic Hecke algebras. I will introduce the combinatorics underlying Webster's diagrammatic
Cherednik algebra and its cellular structure, and discuss how we used isomorphisms between different subquotients to generalise the results of Chuang, Kleshchev,Miyachi, Tan and Teo on decomposition
numbers. Our results on graded decomposition numbers take these level 1 results into higher levels and beyond (applying to many different labellings of simple modules), and apply over fields of arbitrary
characteristic.
|
| Date |
October 5 (Mon.) 18：00～19：30 |
| Speaker |
Takuma Aihara（Tokyo Gakugei University） |
| Title |
準傾連結三角圏 |
| Place |
Osaka City University Academic Extension Center |
| Abstract |
導来圏などの三角圏は、準傾対象によってその構造がコントロールされる。そのような重要な対象を得る方法として、準傾変異が挙げられる。準傾変異は、１つの準傾対象からもう１つの別の準傾対象を構成するものであり、
いつでも可能なため、無数に多くの準傾対象をもたらす。自然な疑問として、「準傾変異によっ て、すべての準傾対象を得られるか？」が挙げられる。本講演では、この疑問に関連する最近の話題を紹介する。
|
| Date |
July 27 (Mon.) 18：00～19：30 |
| Speaker |
Tomoyuki Arakawa (Kyoto University) |
| Title |
Joseph ideal and lisse minimal W-algebras |
| Place |
Osaka City University Academic Extension Center
|
| Abstract |
We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting of affine Kac-Moody algebras and find new examples of affine vertex algebras whose associated varieties
are minimal nilpotent orbit closures. As an application we obtain a new family of lisse (C_2-cofinite) W-algebras that are not coming from admissible representations of affine Kac-Moody algebras. This is
a joint work with Anne Moreau, and is motivated by a recent work of Kawasetsu. |
Last Modified on September 28, 2015
