Osaka Representation Theory Seminar (2011)

List of Osaka Representation Theory Seminar by year
Date January 16 (Mon.) 18：00～19：30
Speaker Andrew Mathas (University of Sydney)
Title Quiver Schur algebras for quivers of type A
Place Osaka City University Academic Extension Center
Abstract Building on work of Khovanov-Lauda and Rouquier, Brundan and Kleshchev showed that the (degenerate and non-degenerate) cyclotomic Hecke algebras of type G(r,1,n) admit a Z-grading. These algebras have a "nice" quasi-hereditary covers, the cyclotomic Schur algebras. I will describe how to lift Brundan and Kleshchev's Z-grading on the Hecke algebra to give a Z-graded algebra which is Morita equivalent to the cyclotomic Schur algebras. The quiver Schur algebras for the linear quiver (which correspond to he Hecke algebras at non roots of unity) are Koszul algebras and their decomposition numbers are independent of the characteristic. Moreover, there is a "nice" LLT-like algorithm for computing the decomposition numbers of these algebras. If time permits I will also explain how to extend the construction of the quiver Schur algebras to the cyclic quiver, which recovers results of Ariki and Stroppel-Webster. This is joint work with Jun Hu.
Date November 21 (Mon.) 18：00～19：30
Speaker PARK, Euiyong (Osaka University)
Title Categorification of quantum generalized Kac-Moody algebras
Place Osaka City University Academic Extension Center
Abstract In this talk, we investigate the structure of the Khovanov-Lauda- Rouquier algebras R and their cyclotomic quotients R^\lambda which give a categrification of quantum generalized Kac-Moody algebras. We also talk about the crystal structure on the set of the isomorphism classes of irreducible graded modules over R and R^\lambda (arXiv:1102.5165 with Kang and Oh). If time permits, I present my recent result on geometric realization of R which is work in progress with Kang and Kashiwara.
Date October 24 (Mon.) 18：00～20：00
Speaker Fang, Ming（The Chinese Academy of Sciences/Osaka University)
Title Endomorphism algebras of generators over symmetric algebras
Place Osaka City University Academic Extension Center
Abstract In this talk, we will introduce a new class of finite dimensional algebras: endomorphism algebras of generators over symmetric algebras.
These algebras appear naturally in Lie theory and also in extending a characterization of dominant dimension. We will mainly illustrate a new (coalgebra without counit) structure on these algebras, and a Hochschild type complex and the use of domiant dimension in studying Hochschild cohomology. Some applications and open problems will also be discussed. (This is a joint work with Steffen Koenig)
Date July 11 (Mon.) 18：00～20：00
Speaker Hiraku Nakajima（Kyoto University, RIMS)
Title Handsaw quiver varieties and finite W-algebras
Place Osaka City University Academic Extension Center
Abstract Following Braverman-Finkelberg-Fegin-Rybnikov (arXiv:1008.3655), we study the convolution algebra of handsaw quiver varieties, a.k.a.　Laumon spaces, and finite W-algebras of type A. A new observation is that their simple modules are described in terms of IC sheaves of graded quiver varieties of type A, which were known to be related to Kazhdan-Lusztig polynomials of type A. This confirms a conjecture by Brundan-Kleshchev.
Date June 20 (Mon.) 18：00～20：00
Speaker Noriyuki Abe　(Hokkaido University)
Title 分裂型p進簡約群の既約許容法p表現の分類について
Place Osaka City University Academic Extension Center
Abstract 分裂型p進簡約群の標数がpの体の上における既約許容表現の分類を，既約許容超尖点表現の分類に帰着させる定理を紹介する．実際には，まず既約超特異表現と呼ばれる表現への分類に帰着させる定理を示し， そのことを用いて，既約許容表現が超特異であることと超尖点であるこが同値であることを示す．これは，GL(2)の場合にBarthel-Livneにより，またGL(n)の場合にHerzigにより得られていた定理の一般化である．
Date May 16 (Mon.) 18：00～19：30
Speaker Osamu Iyama (Nagoya Univ.)
Title Tilting and cluster tilting for stable categories of Cohen-Macaulay modules
Place Osaka City University Academic Extension Center
Abstract Representation theory of CM (=Cohen-Macaulay) modules were initiated by Auslander-Reiten. The stable categories of CM modules were recently studied by many people as singular derived categories (Goresntein case) and as stable categories of matrix factorizations (hypersurface case). I will explain their properties in the context of tilting theory as well as cluster tilting theory. In particular we will see that the stable categories of graded (resp. ungraded) CM modules are often realized as derived (resp. cluster) categories of certain algebras by using tilting (resp. cluster tilting) theory.
Date April 19 (Tue.) 18：00～19：30
Speaker Ryoichi Kase (Osaka University)
Title 道代数における傾斜箙の辺の個数について
Place Osaka City University Academic Extension Center
Abstract ある基本的傾斜加群から別の基本的傾斜加群を作る変異という操作があるが、傾斜箙とは基本的傾斜加群を頂点とし、変異元から変異先へと有向辺を引く事により得られる箙である。今、代数閉体上の有限次元道代数に おいて傾斜箙が有限型であることと道代数がDynkin型であることが同値となることが知られており、頂点の個数はFomin-Zelevinskiの論文等で得られている。今回の講演では道代数の傾斜箙の辺の個数が代数を定める箙の辺の 向き付けによらないこと及びA型、D型の場合の具体的な辺の個数について紹介し、証明の概略を述べたいとおもう。なお、これはarXiv:1101.4747で公表している内容である。
Last Modified on December 15, 2011