Table of Contents
ISRN Combinatorics
Volume 2013, Article ID 431024, 17 pages
http://dx.doi.org/10.1155/2013/431024
Research Article

Crystal Bases as Tuples of Integer Sequences

Mathematisches Institut, Universität zu Köln, 50931 Köln, Germany

Received 31 January 2013; Accepted 19 February 2013

Academic Editors: M. Caramia and R. Dondi

Copyright © 2013 Deniz Kus. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We describe a set consisting of tuples of integer sequences and provide certain explicit maps on it. We show that this defines a semiregular crystal for and , respectively. Furthermore, we define for any dominant integral weight a connected subcrystal in , such that this crystal is isomorphic to the crystal graph . Finally, we provide an explicit description of these connected crystals .