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PBW bases and marginally large tableaux in types B and C

  • Jackson Criswell,
    Central Michigan University , Mount Pleasant, MI 48859 , United States
  • Ben Salisbury,
    Central Michigan University , Mount Pleasant, MI 48859 , United States
  • Peter W. Tingley,
    Dept. of Math and Stats, Loyola University Chicago , Chicago, IL 60660 , United States
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Abstract

We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara's infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions coming from PBW bases. We also discuss a stack notation for Kostant partitions which simplifies that realization.
Keywords: crystal, Kostant partition, Lusztig data, marginally large tableau crystal, Kostant partition, Lusztig data, marginally large tableau
MSC Classifications: 05E10, 17B37 show english descriptions Combinatorial aspects of representation theory [See also 20C30]
Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
05E10 - Combinatorial aspects of representation theory [See also 20C30]
17B37 - Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
 

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