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Abstract view

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

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 $(-1,0)$).