Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165



Existence of Kirillov鈥揜eshetikhin crystals for nonexceptional types

Authors: Masato Okado and Anne Schilling
Journal: Represent. Theory 12 (2008), 186-207
MSC (2000): Primary 17B37, 81R50; Secondary 05E15, 81R10
Published electronically: April 14, 2008
Erratum: Represent. Theory 12 (2008), 499-500.
MathSciNet review: 2403558
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using the methods of Kang et al. and recent results on the characters of Kirillov鈥揜eshetikhin modules by Nakajima and Hernandez, the existence of Kirillov鈥揜eshetikhin crystals $B^{r,s}$ is established for all nonexceptional affine types. We also prove that the crystals $B^{r,s}$ of type $B_n^{(1)}$, $D_n^{(1)}$, and $A_{2n-1}^{(2)}$ are isomorphic to recently constructed combinatorial crystals for $r$ not a spin node.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 17B37, 81R50, 05E15, 81R10

Retrieve articles in all journals with MSC (2000): 17B37, 81R50, 05E15, 81R10

Additional Information

Masato Okado
Affiliation: Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

Anne Schilling
Affiliation: Department of Mathematics, University of California, One Shields Avenue, Davis, California 95616-8633
MR Author ID: 352840
ORCID: 0000-0002-2601-7340

Received by editor(s): August 8, 2007
Received by editor(s) in revised form: February 26, 2008
Published electronically: April 14, 2008
Dedicated: Dedicated to Professor Masaki Kashiwara on his sixtieth birthday
Article copyright: © Copyright 2008 American Mathematical Society