Simplicity of heads and socles of tensor products

By Seok-Jin Kang, Masaki Kashiwara, Myungho Kim, Se-jin Oh. Compositio Mathematica, 2014

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Abstract 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0fc5fe73b510832ec1f2f21381eff656a37afed5