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HIGHEST WEIGHT VECTORS OF IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERALGEBRA μq(gl(m, n))
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 Title & Authors
HIGHEST WEIGHT VECTORS OF IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERALGEBRA μq(gl(m, n))
Moon, Dong-Ho;
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 Abstract
The Iwahori-Hecke algebra ( ) of type A acts on the k-fold tensor product space of the natural representation of the quantum superalgebra (equation omitted)(gl(m, n)). We show the Hecke algebra ( ) and the quantum superalgebra (equation omitted)(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.t space.
 Keywords
quantum superalgebra;maximal vector;Hecke algebra;Schur-Weyl duality;
 Language
English
 Cited by
1.
Presenting Schur superalgebras, Pacific Journal of Mathematics, 2013, 262, 2, 285  crossref(new windwow)
2.
Mixed Tensor Representations of Quantum Superalgebra q(gl(m,n)), Communications in Algebra, 2007, 35, 3, 781  crossref(new windwow)
3.
Quantum Schur superalgebras and Kazhdan–Lusztig combinatorics, Journal of Pure and Applied Algebra, 2011, 215, 11, 2715  crossref(new windwow)
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