Subrepresentations in the Polynomial Representation of the Double Affine Hecke Algebra of type GL_n at t^k+1q^r-1=1

2005/01/18 by Kasatani, Masahiro
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0501272

Abstract

We study a Laurent polynomial representation V of the double affine Hecke algebra of type GL_n for specialized parameters t^k+1q^r-1=1. We define a series of subrepresentations of V by using a vanishing condition. For some cases, we give an explicit basis of the subrepresentation in terms of nonsymmetric Macdonald polynomials. These results are nonsymmetric versions of \citeFJMM and \citeKMSV.

Related

• The polynomial representation of the double affine Hecke algebra of type (C^\vee_n, C_n) for specialized parameters
• Non-semisimple Macdonald polynomials
• Representations of Degenerate Affine Hecke Algebra of Type C_n Under the Etingof-Freund-Ma Functor
• Clebsch-Gordan coefficients for Macdonald polynomials
• Quasi-polynomial representations of double affine Hecke algebras