<p> 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. </p><p> We also investigate Ram's version of Schwer's formula for Hall-Littlewood <i> P</i>-polynomials in type <i>A,</i> 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.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:3594475 |
| Date | 30 October 2013 |
| Creators | Lubovsky, Arthur |
| Publisher | State University of New York at Albany |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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