English

Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules

Quantum Algebra 2007-05-23 v2 Combinatorics Representation Theory

Abstract

We give a general way of representing the crystal (base) corresponding to the intgrable highest weight modules of quantum Kac-Moody algebras, which is called polyhedral realizations. This is applied to describe explicitly the crystal bases of integrable highest weight modules for arbitrary rank 2 Kac-Moody algebra cases, the classical A_n-case and the affine A^{(1)}_{n-1}-case.

Keywords

Cite

@article{arxiv.math/9806085,
  title  = {Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules},
  author = {Toshiki Nakashima},
  journal= {arXiv preprint arXiv:math/9806085},
  year   = {2007}
}

Comments

LaTeX, 27 pages, some reference is added

R2 v1 2026-07-22T17:58:55.623Z