Zhu's algebra and the C_{2}algebra in the symplectic and the orthogonal cases
Abstract
We prove that Zhu's algebra and the C_{2}algebra of type {\tt C}_m have the same dimension, and we compute the graded character of the latter. Maximal parabolic subalgebras of the symplectic algebra play a central role in our construction. For the orthogonal algebras our methods do not allow us to describe the whole C_{2}algebras; we get only a description of a certain quotient of the algebra.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 2010
 DOI:
 10.1088/17518113/43/13/135206
 arXiv:
 arXiv:0911.2957
 Bibcode:
 2010JPhA...43m5206F
 Keywords:

 Mathematics  Representation Theory;
 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 19 pages