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Simplicity of heads and socles of tensor products
- Part of
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 2 / February 2015
- Published online by Cambridge University Press:
- 26 November 2014, pp. 377-396
- Print publication:
- February 2015
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- Article
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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.
