Nonsymmetric Macdonald polynomials and Demazure characters
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We establish a connection between a specialization of the nonsymmetric Macdonald polynomials and the Demazure characters of the corresponding affine Kac-Moody algebra. This allows us to obtain a representation-theoretical interpretation of the coefficients of the expansion of the specialized symmetric Macdonald polynomials in the basis formed by the irreducible characters of the associated finite Lie algebra.
16 pages
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), 33D80, nonsymmetric Macdonald polynomials, 33D45, Demazure characters, 17B67, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Hecke algebras and their representations, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, symmetric Macdonald polynomials, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), double affine Hecke algebra, Representation Theory (math.RT), Koornwinder polynomials, intertwiners., Mathematics - Representation Theory
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), 33D80, nonsymmetric Macdonald polynomials, 33D45, Demazure characters, 17B67, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Hecke algebras and their representations, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, symmetric Macdonald polynomials, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), double affine Hecke algebra, Representation Theory (math.RT), Koornwinder polynomials, intertwiners., Mathematics - Representation Theory
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