## Mixed hook-length formula for degenerate affine Hecke algebras

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Title of host publication | Asymptotic Combinatorics with Applications to Mathematical Physics |
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Date | Published - 1 Jan 2003 |
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Pages | 223-236 |
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Number of pages | 14 |
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Publisher | Springer Berlin / Heidelberg |
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Place of Publication | BERLIN |
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Editors | Anatoly Vershik, Yuri Yakubovich |
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Volume | 1815/2003 |
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Original language | English |
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ISBN (Print) | 978-3-540-40312-8 |
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Name | Lecture Notes in Mathematics |
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Publisher | Sprinter |
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Volume | 1815/2003 |
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ISSN (Print) | 0075-8434 |
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ISSN (Electronic) | 1617-9692 |
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Take the degenerate a fine Hecke algebra H l+m corresponding to the group GL l +m over a p-adic field.Consider the H l+m -module W induced from the tensor product of the evaluation modules over the algebras H l x and H m .The module W depends on two partitions ¿ of l and µ of m, and on two complex numbers.There is a canonical operator J acting in W, it corresponds to the Yang R-matrix.The algebra H l+m contains the symmetric group algebra C S l +m as a subalgebra, and J commutes with the action of this subalgebra in W. Under this action,W decomposes into irreducible subspaces according to the Littlewood — Richardson rule. We compute the eigenvalues of J, corresponding to certain multiplicity-free irreducible components of W. In particular,we give a formula for the ratio of two eigenvalues of J, corresponding to the maximal and minimal irreducible components. As an application of our results,we derive the well-known hook-length formula for the dimension of the irreducible C S l -module corresponding to ¿.

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