Vertex algebra module theory made easy-ish
Simon Wood (Cardiff University)
Wednesday 22nd November, 2017 16:00-17:00 Maths 311B
Abstract
Vertex algebras form the rigorous algebraic underpinning of 2
dimensional conformal field theory. A vertex algebra is said to be rational if
it admits only finitely many simple modules up to isomorphism and if all
modules are semisimple. The module categories of such rational vertex algebras
are examples of modular tensor categories and it is conjectured that every
modular tensor category is the module category for some vertex algebra. While
this categorical picture is certainly beautiful, one can argue that it
obscures the fact that actually classifying the simple modules of a vertex
algebra and verifying rationality is indeed a very hard problem. In this talk
I will present some recent on work classifying simple modules for certain
types of vertex algebras which transforms hard representation theory question
into comparatively easy ones involving the combinatorics of symmetric
polynomials. No prior knowledge of vertex algebras will be assumed.
it admits only finitely many simple modules up to isomorphism and if all
modules are semisimple. The module categories of such rational vertex algebras
are examples of modular tensor categories and it is conjectured that every
modular tensor category is the module category for some vertex algebra. While
this categorical picture is certainly beautiful, one can argue that it
obscures the fact that actually classifying the simple modules of a vertex
algebra and verifying rationality is indeed a very hard problem. In this talk
I will present some recent on work classifying simple modules for certain
types of vertex algebras which transforms hard representation theory question
into comparatively easy ones involving the combinatorics of symmetric
polynomials. No prior knowledge of vertex algebras will be assumed.
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