Dissertation/Thesis Abstract

Alcove models for Hall-Littlewood polynomials and affine crystals
by Lubovsky, Arthur, Ph.D., State University of New York at Albany, 2013, 66; 3594475
Abstract (Summary)

The alcove model of Cristian Lenart and Alexander Postnikov describes highest weight crystals of semisimple Lie algebras in terms of so-called alcove walks. We present a generalization, called the quantum alcove model, which has been related to tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types.

We also investigate Ram's version of Schwer's formula for Hall-Littlewood P-polynomials in type A, which is expressed in terms of the alcove model. We connect it to a formula similar in flavor to the Haglund-Haiman-Loehr formula, which is expressed in terms of fillings of Young diagrams.

Indexing (document details)
Advisor: Lenart, Cristian
Commitee: Milas, Antun, Tchernev, Alexandre
School: State University of New York at Albany
Department: Mathematics
School Location: United States -- New York
Source: DAI-B 75/01(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Affine crystals, Hall-littlewood polynomials, Kirillov-reshetikhin crystals, Quantum alcove model, Quantum bruhat graph
Publication Number: 3594475
ISBN: 978-1-303-38956-6
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