SEMINAR: Groups and Combinatorics Seminar, Decomposing tensor products over fields of small characteristic


Groups and Combinatorics Seminar, Decomposing tensor products over fields of small characteristic 
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Abstract:
One motivation for this talk comes from representation theory: decomposing a tensor product of irreducible (or indecomposable) representations as a sum of smaller degree irreducible (or indecomposable) representations. Other motivations come from quantum mechanics and Frobenius algebras.
Consider an $r imes r$ matrix $K_r$ over a field $F$ with 1s on the main diagonal and first upper diagonal (positions $(i,i)$ and $(i,i+1)$) and zeros elsewhere. The tensor product $K_r times K_s$ is a unipotent matrix whose Jordan canonical form is determined by some partition of $rs$. We will show that this partition enjoys surprising symmetries: duality, periodicity, regularity. Our original motivation was to study this partition when the characteristic $p$ of $F$ is small (i.e. $p<r+s1$). The large characteristic case ($p e r+s1$) was solved recently by Iima and Iwamatsu.
This is joint work with Cheryl E. Praeger and Binzhou Xia.
Speaker(s) 
Stephen Glasby (UWA)

Location 
Weatherburn Lecture Theatre


Contact 
Irene Pivotto
<[email protected]>

Start 
Fri, 16 Aug 2013 15:00

End 
Fri, 16 Aug 2013 16:00

Submitted by 
Irene Pivotto <[email protected]>

Last Updated 
Wed, 02 Oct 2013 16:08

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