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# Fermionic and Bosonic Representations of the Extended Affine Lie Algebra $\widetilde{\mathfrak{gl}_N} (\mathbb{C}_q)$

Published:2002-12-01
Printed: Dec 2002
• Yun Gao
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## Abstract

We construct a class of fermions (or bosons) by using a Clifford (or Weyl) algebra to get two families of irreducible representations for the extended affine Lie algebra $\widetilde{\mathfrak{gl}_N (\mathbb{C}_q)}$ of level $(1,0)$ (or $(-1,0)$).
 MSC Classifications: 17B65 - Infinite-dimensional Lie (super)algebras [See also 22E65] 17B67 - Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras