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Simplicity of heads and socles of tensor products

Part of: Lie algebras and Lie superalgebras Groups and algebras in quantum theory

Published online by Cambridge University Press:  26 November 2014

Seok-Jin Kang ,
Masaki Kashiwara ,
Myungho Kim  and
Se-jin Oh
Seok-Jin Kang
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea email sjkang@snu.ac.kr
Masaki Kashiwara
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea email masaki@kurims.kyoto-u.ac.jp
Myungho Kim
Affiliation:
School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Korea email mhkim@kias.re.kr
Se-jin Oh
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea email sj092@snu.ac.kr
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Abstract

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We prove that, for simple modules $M$ and $N$ over a quantum affine algebra, their tensor product $M\otimes N$ has a simple head and a simple socle if $M\otimes M$ is simple. A similar result is proved for the convolution product of simple modules over quiver Hecke algebras.

Keywords

quantum affine algebraKhovanov–Lauda–Rouquier algebraR-matrix

MSC classification

Primary: 81R50: Quantum groups and related algebraic methods 17B37: Quantum groups (quantized enveloping algebras) and related deformations
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 2 , February 2015 , pp. 377 - 396
Copyright
© The Author(s) 2014 

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