Subrepresentations in the Polynomial Representation of the Double Affine Hecke Algebra of type GLn at tk+1qr-1=1
Masahiro Kasatani
Abstract
We study a Laurent polynomial representation V of the double affine Hecke algebra of type GLn for specialized parameters tk+1qr-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 FJMM and KMSV.
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