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- W4289693899 abstract "In a previous paper J.-G. Luque and the author (Sem. Loth. Combin. 2011) developed the theory of nonsymmetric Macdonald polynomials taking values in an irreducible module of the Hecke algebra of the symmetric group $mathcal{S}_{N}$. The polynomials are parametrized by $left( q,tright) $ and are simultaneous eigenfunctions of a commuting set of Cherednik operators, which were studied by Baker and Forrester (IMRN 1997). In the Dunkl-Luque paper there is a construction of a pairing between $left( q^{-1},t^{-1}right) $ polynomials and $left( q,tright) $ polynomials, and for which the Macdonald polynomials form a biorthogonal set. The present work is a sequel with the purpose of constructing a symmetric bilinear form for which the Macdonald polynomials form an orthogonal basis and to determine the region of $left( q,tright) $-values for which the form is positive-definite. Irreducible representations of the Hecke algebra are characterized by partitions of $N$. The positivity region depends only on the maximum hook-length of the Ferrers diagram of the partition." @default.
- W4289693899 created "2022-08-04" @default.
- W4289693899 creator A5025603833 @default.
- W4289693899 date "2018-08-15" @default.
- W4289693899 modified "2023-10-16" @default.
- W4289693899 title "A positive-definite inner product for vector-valued Macdonald polynomials" @default.
- W4289693899 doi "https://doi.org/10.48550/arxiv.1808.05251" @default.
- W4289693899 hasPublicationYear "2018" @default.
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