Howe Pairs in the Theory of Vertex Algebras
Abstract
For any vertex algebra V and any subalgebra A of V, there is a new subalgebra of V known as the commutant of A in V. This construction was introduced by FrenkelZhu, and is a generalization of an earlier construction due to KacPeterson and GoddardKentOlive known as the coset construction. In this paper, we interpret the commutant as a vertex algebra notion of invariant theory. We present an approach to describing commutant algebras in an appropriate category of vertex algebras by reducing the problem to a question in commutative algebra. We give an interesting example of a Howe pair (ie, a pair of mutual commutants) in the vertex algebra setting.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2006
 arXiv:
 arXiv:math/0605174
 Bibcode:
 2006math......5174L
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra
 EPrint:
 A few typos corrected, final version