In the theory of vertex algebras, there is a notion of commutant subalgebras, which is analogous to the notion of commutant subalgebras of ordinary associative algebras. If V is a vertex algebra and A is any subset of V, the commutant Comm(A,V) is defined and is always a vertex subalgebra. If A, A' are subalgebras of V, and A' = Comm(A,V) and A = Comm(A',V), we say that A and A' form a Howe pair.
In this talk, I will define vertex algebras and show how one can reduce the problem of computing commutant subalgebras to a problem in invariant theory. In particular, describing a commutant subalgebra will be equivalent to giving generators for the invariant subspace of a module over an infinite-dimensional Lie algebra. I will use these ideas to give an example of a Howe pair.
Every graduate student of Mathematics is invited (encouraged!) to give a talk. You most certainly do NOT have to present original work. The talks should be accessible to any bright graduate student, at any level of their studies. You can present a topic that most people may not have heard about, or things people may have heard about but have no idea what it is.
Come to hear new topics, learn new methods, build camaraderie with your fellow graduate students... and most importantly - eat some free pizza!
Page created: Sep. 7th, 2003
Last updated: Apr. 28th, 2004
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