@inbook{2ee5dc10dd5c4d98a11f5ae020f54b57,
title = "Mixed hook-length formula for degenerate affine Hecke algebras",
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 ¿. ",
author = "Maxim Nazarov",
year = "2003",
month = jan,
day = "1",
doi = "10.1007/3-540-44890-X_10",
language = "English",
isbn = "978-3-540-40312-8",
volume = "1815/2003",
series = "Lecture Notes in Mathematics",
publisher = "Springer",
pages = "223--236",
editor = "Anatoly Vershik and Yuri Yakubovich",
booktitle = "Asymptotic Combinatorics with Applications to Mathematical Physics",
address = "Germany",
note = "Conference of the NATO-Advanced-Study-Institute on Asymptotic Combinatorics with Application to Mathematical Physics ; Conference date: 09-07-2001 Through 22-07-2001",
}