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.
|Commitee:||Milas, Antun, Tchernev, Alexandre|
|School:||State University of New York at Albany|
|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|
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