English

Crystal $\Bla$ in $B(\infty)$ for $G_2$ type Lie Algebra

Representation Theory 2013-10-24 v1 Quantum Algebra

Abstract

A previous work gave a combinatorial description of the crystal B()B(\infty), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal B(λ)B(\lambda), in terms of the marginally large tableaux, for the G2G_2 Lie algebra type. We also provide a new description of B(\la)B(\la), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.

Keywords

Cite

@article{arxiv.1310.6211,
  title  = {Crystal $\Bla$ in $B(\infty)$ for $G_2$ type Lie Algebra},
  author = {Min Kyu Kim and Hyeonmi Lee},
  journal= {arXiv preprint arXiv:1310.6211},
  year   = {2013}
}

Comments

13 pages, submitted

R2 v1 2026-06-22T01:52:26.724Z