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

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Today's date is Saturday, October 24, 2020
Groups and Combinatorics Seminar, Decomposing tensor products over fields of small characteristic Other events...
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. $p<r+s-1$). The large characteristic case ($p e r+s-1$) 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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