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An explicit construction of type A Demazure atoms. (English) Zbl 1210.05175
Summary: Demazure characters of type A, which are equivalent to key polynomials, have been decomposed by Lascoux and Schützenberger into standard bases. We prove that the resulting polynomials, which we call Demazure atoms, can be obtained from a certain specialization of nonsymmetric Macdonald polynomials. This combinatorial interpretation for Demazure atoms accelerates the computation of the right key associated to a semi-standard Young tableau. Utilizing a related construction, we provide a new combinatorial description of the key polynomials.

MSC:
05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
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