An explicit construction of type A Demazure atoms

By Sarah K. Mason. 2007

102 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/33c93b1230cdaec2f0175aa5b81bdde9cab0b3d7

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

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Citations in the corpus

Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture (2016, methodology): “Although this recursive construction (the Demazure Character Formula) could be used to prove some of our results, Mason’s [24] combinatorial interpretation of Demazure characters in terms of SSK will be crucial in our work.”
Refinements of the Littlewood-Richardson rule (2009, background): “Mason [15],[16] showed that many of the interesting properties of Demazure characters and atoms can be explained via the combinatorics of skyline fillings.”