## 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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