Virtual Crystals and Kleber's Algorithm
Abstract
Kirillov and Reshetikhin conjectured what is now known as the fermionic formula for the decomposition of tensor products of certain finite dimensional modules over quantum affine algebras. This formula can also be extended to the case of qdeformations of tensor product multiplicities as recently conjectured by Hatayama et al. In its original formulation it is difficult to compute the fermionic formula efficiently. Kleber found an algorithm for the simplylaced algebras which overcomes this problem. We present a method which reduces all other cases to the simplylaced case using embeddings of affine algebras. This is the fermionic analogue of the virtual crystal construction by the authors, which is the realization of crystal graphs for arbitrary quantum affine algebras in terms of those of simplylaced type.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2003
 DOI:
 10.1007/s002200030855z
 arXiv:
 arXiv:math/0209082
 Bibcode:
 2003CMaPh.238..187O
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 Mathematics  Combinatorics;
 81R50;
 17B37;
 05A19;
 05A30;
 82B23
 EPrint:
 23 pages