Polyhedral Realizations of Crystal Bases and Braid-type Isomorphisms
Quantum Algebra
2007-05-23 v1 Combinatorics
Representation Theory
Abstract
We review the polyhedral realizations of crystal bases in the former half and in the latter half, we introduce braid-type isomorphisms for some rank 2 finite type crystals. Using this isomorphisms, for semi-simple Lie algebra we can show that polyhedral realizations can be obtained in the lattice of finite rank which coincides with the length of the longest element in the associated Weyl group.
Cite
@article{arxiv.math/9906100,
title = {Polyhedral Realizations of Crystal Bases and Braid-type Isomorphisms},
author = {Toshiki Nakashima},
journal= {arXiv preprint arXiv:math/9906100},
year = {2007}
}
Comments
LaTeX(2e), 19 pages