Fall, 2005
- Speaker Corina Calinescu, Rutgers University
- Title On certain principal subspaces of standard
modules and vertex operator algebras
- Time/place Friday, 9/30/2005 1:00 pm in Hill 705
- Abstract Recently, S. Capparelli, J. Lepowsky and
A. Milas initiated a new
approach of getting Rogers-Ramanujan-type recursions by studying the
principal subspaces of the standard sl(2)^-modules. We extend their
approach to the untwisted affine Lie algebra sl(3)^. In this talk we
give a complete list of relations for the principal subspaces of the
standard sl(3)^-modules. Then, as a consequence of this result and
vertex operator algebra techniques we obtain certain recursions. By
solving them, we recover the graded dimensions (characters) of these
principal subspaces.
- Speaker Katrina Barron, University of Notre Dame
- Title An isomorphism between two constructions of
permutation-twisted modules for lattice vertex operator algebras
- Time/place Friday, 10/14/2005 1:00 pm in Hill 705
- Abstract Twisted modules for vertex operator algebras
arise in physics as the
basic building blocks for ``orbifold" conformal field theory, and
arise in mathematics in the representation theory of
infinite-dimensional Lie algebras. In this talk, we will consider two
constructions of twisted modules in the case of the k-fold tensor
product of a lattice vertex operator algebra with itself and a
permutation automorphism acting on this tensor product. One of these
two constructions involves an operator based on the lattice, and the
second involves an operator based on a coordinate transformation of
the underlying conformal geometry modeled on propagating strings.
However, by a theorem of the speaker, jointly with Dong, and Mason,
they must produce isomorphic twisted modules. We construct an
isomorphism explicitly thereby, from the point of view of physics,
giving a direct link between the space-time geometry arising from the
lattice and the conformal worldsheet geometry of propagating strings.
This is joint work with James Lepowsky and Yi-Zhi Huang.
- Speaker Lin Zhang, Sequent Capital LLC
- Title Kazhdan-Lusztig's tensor category and the
compatibility condition
- Time/place Friday, 10/21/2005 1:00 pm in Hill 705
- Abstract We study from the viewpoint of vertex operator
algebras a braided
tensor category of Kazhdan and Lusztig based on certain modules for an
affine Lie algebra, by using a recent logarithmic generalization, due
to Huang, Lepowsky and Zhang, of Huang and Lepowsky's tensor product
theory for modules for a vertex operator algebra. We first give an
equivalent form of the ``compatibility condition,'' one of the
important tools in the theory of Huang and Lepowsky, in terms of a
``strong lower truncation condition.'' We use this to establish the
equivalence of the two tensor product functors constructed in the two
totally different approaches. Then, by using certain generalized
Knizhnik-Zamolodchikov equations, we prove the ``convergence and
expansion properties'' for this category and obtain a new construction
of the braided tensor category structure. Compared to the original
algebraic-geometric method, the vertex algebraic approach further
establishes a vertex tensor category structure on this category.
- Speaker Siddhartha Sahi, Rutgers University
- Title Supercategories and connections
- Time/place Friday, 11/11/2005 1:00 pm in Hill 705
- Abstract We introduce the notion of a supercategory as
a generalization of the
tensor category of vector superspaces. We also define the concept of a
"connection" in this context, and prove a series of extremely general
quasi-isomorphism results generalizing the Harish-Chandra isomorphism.
- Speaker Hisham Sati, University of Adelaide
- Title Mathematical aspects of the partition functions
in string theory
- Time/place Friday, 12/16/2005 1:00 pm in Hill 705
- Abstract
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