Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures

Details Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures

2010-01-14

arxiv.org/abs/1001.2345v2

Mathematics

Combinatorics

36 pages. v2: minor correction

Scientific paper

10.1007/s11139-011-9317-y

We study symmetric polynomials whose variables are odd-numbered Jucys-Murphy elements. They define elements of the Hecke algebra associated to the Gelfand pair of the symmetric group with the hyperoctahedral group. We evaluate their expansions in zonal spherical functions and in double coset sums. These evaluations are related to integrals of polynomial functions over orthogonal groups. Furthermore, we give an extension of them, based on Jack polynomials.

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