Simplicity of heads and socles of tensor products

Seok Jin Kang; Masaki Kashiwara; Myungho Kim; Se Jin Oh

doi:10.1112/S0010437X14007799

Simplicity of heads and socles of tensor products

Seok Jin Kang, Masaki Kashiwara, Myungho Kim, Se Jin Oh

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

65 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	377-396
Number of pages	20
Journal	Compositio Mathematica
Volume	151
Issue number	2
DOIs	https://doi.org/10.1112/S0010437X14007799
State	Published - 25 Feb 2015

Bibliographical note

Publisher Copyright:
© 2014 Foundation Compositio Mathematica.

Keywords

Khovanov-Lauda-Rouquier algebra
R-matrix
quantum affine algebra

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10.1112/S0010437X14007799

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

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AU - Kim, Myungho

AU - Oh, Se Jin

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

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KW - R-matrix

KW - quantum affine algebra

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Simplicity of heads and socles of tensor products

Abstract

Bibliographical note

Keywords

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