Polyhedral Realizations of Crystal Bases for Quantized Kac-Moody Algebras
q-alg
2016-09-08 v1 Quantum Algebra
Abstract
Let B(\infty) be the crystal corresponding to the nilpotent part of a quantized Kac-Moody algebra. We suggest a general way to represent B(\infty) as the set of integer solutions of a system of linear inequalities. As an application, we treat in a unified manner all Kac-Moody algebras of rank 2 (sharpening the result by Kashiwara), as well as the algebras of types A_n and A_{n-1}^{(1)}.
Cite
@article{arxiv.q-alg/9703045,
title = {Polyhedral Realizations of Crystal Bases for Quantized Kac-Moody Algebras},
author = {Toshiki Nakashima and Andrei Zelevinsky},
journal= {arXiv preprint arXiv:q-alg/9703045},
year = {2016}
}
Comments
24 pages, LaTeX