JACK POLYNOMIALS AND THE COINVARIANT RING OF G(r, p, n)
نویسنده
چکیده
We study the coinvariant ring of the complex reflection group G(r, p, n) as a module for the corresponding rational Cherednik algebra H and its generalized graded affine Hecke subalgebra H. We construct a basis consisting of non-symmetric Jack polynomials, and using this basis decompose the coinvariant ring into irreducible modules for H. The basis consists of certain non-symmetric Jack polynomials, whose leading terms are the “descent monomials” for G(r, p, n) recently studied by Adin, Brenti, and Roichman and Bagno and Biagoli. The irreducible H-submodules of the coinvariant ring are their “colored descent representations”.
منابع مشابه
Jack Polynomials and the Coinvariant Ring of G
We study the coinvariant ring of the complex reflection group G(r, p, n) as a module for the corresponding rational Cherednik algebra H and its generalized graded affine Hecke subalgebra H. We construct a basis consisting of non-symmetric Jack polynomials, and using this basis decompose the coinvariant ring into irreducible modules forH. The basis consists of certain non-symmetric Jack polynomi...
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