Algebras over a Fock space.

    Yun Gao, (York University)

Abstract: We find that a Fock space which is the basic module for the affine general Lie algebra \hat{gl}__N allows both the quantum affine general algebra U_q(\hat{gl}__N) and the quantum toroidal algebra actions by using the vertex operator construction. As a byproduct, we enhance a Lusztig theorem on quantum affine algebras.

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