Mixed hook-length formula for degenerate affine Hecke algebras

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Publication details

Title of host publicationAsymptotic Combinatorics with Applications to Mathematical Physics
DatePublished - 1 Jan 2003
Pages223-236
Number of pages14
PublisherSpringer Berlin / Heidelberg
Place of PublicationBERLIN
EditorsAnatoly Vershik, Yuri Yakubovich
Volume1815/2003
Original languageEnglish
ISBN (Print)978-3-540-40312-8

Publication series

NameLecture Notes in Mathematics
PublisherSprinter
Volume1815/2003
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

Abstract

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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