Generalized Young Walls for Classical Lie Algebras

Jeong Ah Kim, Dong Uy Shin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we introduce an new combinatorial model, which we call generalized Young walls for classical Lie algebras, and we give two realizations of the crystal B(∞) over classical Lie algebras using generalized Young walls. Also, we construct natural crystal isomorphisms between generalized Young wall realizations and other realizations, for example, monomial realization, polyhedral realization and tableau realization. Moreover, as applications, we obtain a crystal isomorphism between two different polyhedral realizations of B(∞).

Original languageEnglish
Pages (from-to)345-373
Number of pages29
JournalAlgebras and Representation Theory
Volume22
Issue number2
DOIs
StatePublished - 2019 Apr 15

Keywords

  • Crystals
  • Generalized Young walls
  • Kashiwara embeddings
  • Nakajima monomials
  • Tableaux

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