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Simplicity of heads and socles of tensor products

Published online by Cambridge University Press:  26 November 2014

Seok-Jin Kang
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea email [email protected]
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 [email protected]
Myungho Kim
Affiliation:
School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Korea email [email protected]
Se-jin Oh
Affiliation:
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea email [email protected]
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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.

Type
Research Article
Copyright
© The Author(s) 2014 

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