Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials
Abstract
The fusion rule gives the dimensions of spaces of conformal blocks in the WZW theory. We prove a dimension formula similar to the fusion rulefor spaces of coinvariants of affine Lie algebras g^. An equivalence of filtered spaces is established between spaces of coinvariants of two objects: highest weight g^modules and tensor products of finitedimensional evaluation representations of g\otimes\C[t]. In the sl_2 case we prove that their associated graded spaces are isomorphic to the spaces of coinvariants of fusion products, and that their Hilbert polynomials are the levelrestricted Kostka polynomials.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2002
 DOI:
 10.48550/arXiv.math/0205324
 arXiv:
 arXiv:math/0205324
 Bibcode:
 2002math......5324F
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Combinatorics;
 Mathematics  Representation Theory;
 17B65
 EPrint:
 31 pages