• Title/Summary/Keyword: Hecke algebra

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HIGHEST WEIGHT VECTORS OF IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERALGEBRA μq(gl(m, n))

  • Moon, Dong-Ho
    • Journal of the Korean Mathematical Society
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    • v.40 no.1
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    • pp.1-28
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    • 2003
  • The Iwahori-Hecke algebra $H_{k}$ ( $q^2$) of type A acts on the k-fold tensor product space of the natural representation of the quantum superalgebra (equation omitted)$_{q}$(gl(m, n)). We show the Hecke algebra $H_{k}$ ( $q^2$) and the quantum superalgebra (equation omitted)$_{q}$(gl(m n)) have commuting actions on the tensor product space, and determine the centralizer of each other. Using this result together with Gyoja's q-analogue of the Young symmetrizers, we construct highest weight vectors of irreducible summands of the tensor product space.

ON THE TWO SIDED IDEALS OF ORDERS IN A QUATERNION ALGEBRA

  • JUN, SUNG TAE;KIM, IN SUK
    • Honam Mathematical Journal
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    • v.26 no.4
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    • pp.365-378
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    • 2004
  • The orders in quaternion algebras play central role in the theory of Hecke operators. In this paper, we study the order of two sided ideal group in orders of a quaternion algebra.

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