Virtual crystals and Kleber's algorithm
Skip to main content
eScholarship
Open Access Publications from the University of California

Virtual crystals and Kleber's algorithm

  • Author(s): Okado, Masato
  • Schilling, Anne
  • Shimozono, Mark
  • et al.

Published Web Location

https://arxiv.org/pdf/math/0209082.pdf
No data is associated with this publication.
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 $q$-deformations of tensor product multiplicities as recently conjectured by Hatayama et al. (math.QA/9812022 and math.QA/0102113). In its original formulation it is difficult to compute the fermionic formula efficiently. Kleber (q-alg/9611032 and math.QA/9809087) found an algorithm for the simply-laced algebras which overcomes this problem. We present a method which reduces all other cases to the simply-laced 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 simply-laced type.

Item not freely available? Link broken?
Report a problem accessing this item