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2 results

  • Twisted Vertex Operators and Unitary Lie Algebras

  • Fulin Chen, Yun Gao, Naihuan Jing, Shaobin Tan
  • Journal:
    Canadian Journal of Mathematics / Volume 67 / Issue 3 / 01 June 2015
    Published online by Cambridge University Press:
    20 November 2018, pp. 573-596
    Print publication:
    01 June 2015
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  • A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral ${{\mathbb{Z}}_{2}}$-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac–Moody Lie algebra of type $A_{n}^{\left( 2 \right)}$ are recovered by the new method.

  • Representations of Extended Affine Lie Algebras Coordinatized by Certain Quantum Tori

  • Yun Gao
  • Journal:
    Compositio Mathematica / Volume 123 / Issue 1 / August 2000
    Published online by Cambridge University Press:
    04 December 2007, pp. 1-25
    Print publication:
    August 2000
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  • An irreducible representation of the extended affine Lie algebra of type $A_{n-1}$ coordinatized by a quantum torus of ν variables is constructed by using the Fock space for the principal vertex operator realization of the affine Lie algebra ${\widetilde{gl}_{n}$.