An Explicit Construction of Type A Demazure Atoms

Details An Explicit Construction of Type A Demazure Atoms An Explicit Construction of Type A Demazure Atoms

2007-07-28

arxiv.org/abs/0707.4267v2

Journal of Algebraic Combinatorics, Vol. 29, (2009), No. 3, p.295--313

Mathematics

Combinatorics

15 pages; final version

Scientific paper

Demazure characters of type A, which are equivalent to key polynomials, have been decomposed by Lascoux and Sch\"{u}tzenberger 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 for the key polynomials.

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