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Vyjayanthi Chari
vyjayanc at ucr.edu |
Wee Liang Gan
wlgan at math.ucr.edu | Jacob Greenstein
jacobg at ucr.edu |
| May 27, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 |
Charles Conley (University of North Texas)
TBA |
| May 29, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 |
Tanusree Pal (Harish-Chandra Research Institute, India)
Integrable Representations of Graded Multi-loop Lie Algebras Abstract. Let gA be the graded multi-loop Lie algebra and gA(μ) be the graded twisted multi-loop Lie algebra, associated with the simple finite dimensional Lie algebra g over C. In this talk, we describe the isomorphism classes of irreducible integrable gA-modules with finite dimensional weight spaces. We also describe the isomorphism classes of irreducible integrable gA(μ) -modules which are obtained from the above gA-modules by considering the restriction action. The talk is based on a joint work with Punita Batra |
| April 3, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 | Michael Lau (University of Windsor, Canada)
Forms of Conformal Superalgebras Abstract. Conformal superalgebras describe symmetries of superconformal field theories and come equipped with an infinite family of products. They also arise as singular parts of the vertex operator superalgebras associated with some well-known Lie structures (e.g. affine, Virasoro, Neveu-Schwarz). In joint work with Arturo Pianzola and Victor Kac, we classify forms of conformal superalgebras using a non-abelian Cech-like cohomology set. As the products in scalar extensions are not given by linear extension of the products in the base ring, the usual descent formalism cannot be applied blindly. As a corollary, we obtain a rigourous proof of the pairwise non-isomorphism of an infinite family of N=4 conformal superalgebras appearing in mathematical physics. |
| April 8, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 | Bernard Leclerc (Université de Caen, France)
Introduction to cluster algebras Abstract. I will give a quick introduction to the theory of cluster algebras introduced by Fomin and Zelevinsky. I will illustrate it by examples like coordinate rings of unipotent groups and flag varieties. |
| April 10, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 | Bernard Leclerc (Université de Caen, France)
Monoidal categorifications of cluster algebras Abstract. I will introduce the notion of monoidal categorification of a cluster algebra, and will give examples coming from the representation theory of quantum affine algebras. |
| April 17, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 | Bernhard Keller (Université Paris 7, France)
Generalized cluster categories, after C. Amiot Abstract. Fomin and Zelevinsky invented cluster algebras in 2000. Soon, it became clear that these new algebras were intimately related to quiver representations. Cluster categories, introduced in 2004, have provided a beautiful framework for making this relation precise. However, cluster categories are only defined for quivers without oriented cycles. Building on Derksen-Weyman-Zelevinsky's fundamental work on quivers with potentials Claire Amiot has recently been able to extend the construction of the cluster category to a large class of quivers admitting oriented cycles and endowed with a potential, namely the so-called Jacobi-finite quivers with potential. I will report on her results and their links to previous work, due notably to Geiss-Leclerc-Schroer and Buan-Iyama-Reiten-Scott. |
| April 22, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 | Tim Ridenour
On abelian ideals in root systems of simple Lie algebras Abstract. It is a well known result due to D. Peterson that the number of abelian ideals in the positive roots of a simple Lie algebra of rank n is 2n. In this talk, I will discuss general results for ideals in simple Lie algebras including generalizations to k-nilpotent ideals. Furthermore, I will give the details of a simple proof of Peterson’s theorem and give a method for explicitly defining all such ideals. |
| April 29, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 | Henning Haahr Andersen (University of Aarhus, Denmark)
Some applications of tilting modules for quantum groups Abstract. Let Uq denote a quantum group associated to a finite dimensional semi-simple complex Lie algebra.The Ringel-Donkin theory of tilting modules gives for each dominant weight λ a unique indecomposable tilting module T(λ) with highest weight λ. In the generic case these modules are just the finite dimensional irreducible modules but when q is a root of unity we get new interesting modules for Uq. We shall show that they play a crucial role for instance in the theory of quantum invariants for 3-manifolds, in the theory of (quantum) Schur algebras at roots of unity. |
| May 6, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 |
Sergei Loktev (ITEP, Russia)
Representations of mutli-variable currents and a generalization of the Catalan and Narayana numbers Abstract. For each partition we construct a natural representation of the Lie algebra of matrix-valued polynomials. We discuss universality properties of these repreresntations as well as combinatorics of their characters. We present explicit answers for currents in up to three variables. |
| May 8, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 |
Dmitriy Boyarchenko (University of Chicago)
Character sheaves on unipotent groups in characteristic p>0 (joint work with Vladimir Drinfeld) Abstract. Let G be a connected unipotent group over an algebraically closed field k of characteristic p>0. We define a collection of irreducible conjugation-equivariant perverse sheaves on G, which we call character sheaves. The set of all character sheaves naturally decomposes as a disjoint union of finite subsets, called L-packets of character sheaves. We will explain a construction of a large collection of L-packets of character sheaves on G (conjecturally, all of them) in terms of very concrete geometric objects related to G, namely, pairs consisting of a connected subgroup H of G and a multiplicative (rank 1) local system on H, satisfying a suitable analogue of Mackey's irreducibility criterion. This construction can be viewed as a geometric analogue of the classical result that all irreducible representations of a finite nilpotent group are induced from 1-dimensional representations of suitable subgroups. If time permits, we will discuss the case where k is an algebraic closure of a finite field F, and the unipotent group G can be defined over F. In this case, there exists a relationship between irreducible characters of the finite group G(F) and character sheaves on G (just as in Lusztig's theory for reductive groups). In particular, the notion of an L-packet of irreducible characters of G(F) can also be defined. |
| May 13, 2008 | ||
| 1:00-2:00 p.m. | Surge 284 |
Eugene Mukhin (Indiana University - Purdue University Indianapolis)
Bethe Ansatz and around Abstract. The Bethe Ansatz is a method to find eigenvectors of a certain family of commutative matrices. This method is often more complicated than the standard methods of linear algebra, moreover, sometimes it fails to produce the complete set of the eigenvectors. However, the attempts to understand it lead to a number of interesting connections with surprisingly many areas of mathematics - and to new results in those areas. In this talk I will try to give an introduction to the Bethe Ansatz method. |
