Irreducibility of Perfect Representations of Double Affine Hecke Algebras

Details Irreducibility of Perfect Representations of Double Affine Hecke Algebras Irreducibility of Perfect Representations of Double Affine Hecke Algebras

2004-06-16

arxiv.org/abs/math/0406317v2

Mathematics

Quantum Algebra

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We prove that the quotient of the polynomial representation of the double affine Hecke algebra (DAHA) by the radical of the duality pairing is always irreducible assuming that it is finite dimensional (apart from the roots of unity). We also find necessary and sufficient conditions for the radical to be zero, which is a q-generalization of Opdam's formula for the singular k-parameters with the multiple zero-eigenvalues of the corresponding Dunkl operators.

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