On the connection between Macdonald polynomials and Demazure characters (Q1577532)

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.