Affiliation: Department of Mathematics University of California One Shields Ave Davis, CA 95616
Email: anne@math.ucdavis.edu
Title Of Talk: Virtual Kleber algorithm
URL: http://xxx.lanl.gov/abs/math.QA/0209082
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.. From the physics perspective, fermionic formulas are desirable as they reflect the particle content of the underlying model. In its original formulation it is difficult to compute the fermionic formula efficiently. Kleber 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, which is the realization of crystal graphs for arbitrary quantum affine algebras in terms of those of simply-laced type.
Last update made Tue Feb 11 23:01:01 EST 2003.
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