2004/06/16 by Ivan Cherednik, Cherednik, Ivan
Chemistry · Physics and Astronomy · #FOS: Mathematics #Molecular spectroscopy and chirality #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #Quantum optics and atomic interactions #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.math/0406317
openalex publication_date 2004/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.