Double affine Hecke algebras, conformal coinvariants and Kostka polynomials
نویسندگان
چکیده
منابع مشابه
Double Affine Hecke Algebras, Conformal Coinvariants and Kostka Polynomials
We study a class of representations called “calibrated representations” of the degenerate double affine Hecke algebra and those of the rational Cherednik algebra of type GLn. We give a realization of calibrated irreducible modules as spaces of coinvariants constructed from integrable modules over the affine Lie algebra ĝl m . Moreover, we give a character formula of these irreducible modules in...
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It was conjectured by Haiman [H] that the space of diagonal coinvariants for a root system R of rank n has a ”natural” quotient of dimension (1 + h) for the Coxeter number h. This space is the quotient C[x, y]/(C[x, y]C[x, y]o ) for the algebra of polynomials C[x, y] with the diagonal action of the Weyl group on x ∈ C ∋ y and the ideal C[x, y]o ⊂ C[x, y] of the W -invariant polynomials without ...
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In this paper we derive the bi-orthogonality relations, diagonal term evaluations and evaluation formulas for the non-symmetric Koornwinder polynomials. For the derivation we use certain representations of the (double) affine Hecke algebra which were originally defined by Noumi and Sahi. We furthermore give the explicit connection between the non-symmetric and the symmetric theory. This leads i...
متن کاملIntertwining operators of double affine Hecke algebras
Continuing [C3,C4], we study the intertwining operators of double affine Hecke algebras H. They appeared in several papers (especially in [C2,C4,C6]). However for the first time here we apply them systematically to create the nonsymmetric [M3,C4] and symmetric [M2] Macdonald polynomials for arbitrary root systems and to start the theory of induced and co-spherical H-modules. The importance of t...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2006
ISSN: 1631-073X
DOI: 10.1016/j.crma.2006.08.009