Two dimensional current algebras and affine fusion product
Abstract
In this paper we study a family of commutative algebras generated by two infinite sets of generators. These algebras are parametrized by Young diagrams. We explain a connection of these algebras with the fusion product of integrable irreducible representations of the affine $sl_2$ Lie algebra. As an application we derive a fermionic formula for the character of the affine fusion product of two modules. These fusion products can be considered as a simplest example of the double affine Demazure modules.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2006
 DOI:
 10.48550/arXiv.math/0607091
 arXiv:
 arXiv:math/0607091
 Bibcode:
 2006math......7091F
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 22 pages