Quantum loop modules

2002/06/28 by Vyjayanthi Chari, Jacob Greenstein · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #msc:17B67

paper · pdf · doi:10.1090/s1088-4165-03-00168-7

published as Represent. Theory 7 (2003), 56-80 · 25 pages, AMSLaTeX

arxiv created 2002/06/28 · openalex publication_date 2003/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the simple infinite-dimensional integrable modules with finite-dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable modules or simple submodules of a loop module of a finite-dimensional simple integrable module and describe the latter class. Their characters and crystal basis theory are discussed in a special case.

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• Littelmann's path crystal and combinatorics of certain integrable slℓ+1 modules of level zero
• A Character Formula for the Category Õ

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