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On the connection between Macdonald polynomials and Demazure characters. (English) Zbl 0957.05106
Nonsymmetric Macdonald polynomials at \(t=0\) are described in terms of operators applied to 1. This leads to an identification between these polynomials and Demazure characters. From here the real character of a Demazure module is easily obtained, as are conditions that a nonsymmetric Macdonald polynomial has nonnegative coefficients. In addition, this paper derives that Kostka polynomials have positive coefficients, Kostka numbers are the multiplicities of the \(\text{sl}(n)\)-modules in certain Demazure modules, and, multiplied by a given factor, the Kostka polynomials are monotonic.

MSC:
05E05 Symmetric functions and generalizations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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