Polyhedral Realizations of Crystal Bases for Quantum Algebras of Finite Types

2005/07/04 by Ayumu Hoshino · 1 citation
Mathematics · #math.QA #math.RT

paper · pdf · doi:10.1063/1.2121308

27 pages, LaTeX

arxiv created 2005/07/04 · arxiv updated 2009/12/01

Abstract

Polyhedral realization of crystal bases is one of the methods for describing the crystal base B(∞) explicitly. This method can be applied to symmetrizable Kac-Moody types. We can also apply this method to the crystal bases B(λ) of integrable highest weight modules and of modified quantum algebras. But, the explicit forms of the polyhedral realizations of crystal bases B(∞) and B(λ) are only given in the case of arbitrary rank 2, of A_n and of A⁽¹⁾_n. So, we will give the polyhedral realizations of crystal bases B(∞) and B(λ) for all simple Lie algebras in this paper.

Cited by

• A new description of the bicrystal B(∞) and the extended crystal