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Representation Theory
Representation Theory
ISSN 1088-4165

 

$t$-analogs of $q$-characters of Kirillov-Reshetikhin modules of quantum affine algebras


Author: Hiraku Nakajima
Journal: Represent. Theory 7 (2003), 259-274
MSC (2000): Primary 17B37; Secondary 81R50, 82B23
Published electronically: July 10, 2003
MathSciNet review: 1993360
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Abstract: We prove the Kirillov-Reshetikhin conjecture concerning certain finite dimensional representations of a quantum affine algebra ${\mathbf U}_q(\widehat{\mathfrak g})$ when $\widehat{\mathfrak g}$ is an untwisted affine Lie algebra of type $ADE$. We use $t$-analog of $q$-characters introduced by the author in an essential way.


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Additional Information

Hiraku Nakajima
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Email: nakajima@kusm.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S1088-4165-03-00164-X
PII: S 1088-4165(03)00164-X
Received by editor(s): April 29, 2002
Published electronically: July 10, 2003
Additional Notes: Supported by the Grant-in-aid for Scientific Research (No.13640019), JSPS
Dedicated: Dedicated to Professor Takushiro Ochiai on his sixtieth birthday
Article copyright: © Copyright 2003 American Mathematical Society