Diagonal Coinvariants and Double Affine Hecke Algebras

Details Diagonal Coinvariants and Double Affine Hecke Algebras Diagonal Coinvariants and Double Affine Hecke Algebras

2003-05-16

arxiv.org/abs/math/0305245v6

Mathematics

Quantum Algebra

The final variant to appear in IMRN

Scientific paper

We establish a q-generalization of Gordon's theorem that the space of diagonal coinvariants has a quotient identified with a perfect representation of the rational double affine Hecke algebra. It leads to a simple proof of his theorem and relates it to the Weyl algebras at roots of unity. The universal double affine Hecke algebra and the corresponding universal double Dunkl operators acting in noncommutative polynomials in terms of two sets of variables are introduced.

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