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Two dimensional current algebras and affine fusion product

B. Feigin·E. Feigin
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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.

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B. Feigin, E. Feigin. 2006-07-04. Two dimensional current algebras and affine fusion product. https://arxiv.org/abs/math/0607091

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