SEMINAR: Groups and Combinatorics Seminar 16:00 Fri 17/11/2017 Weatherburn LT: Stephen Glasby (UWA)


Groups and Combinatorics Seminar 16:00 Fri 17/11/2017 Weatherburn LT: Stephen Glasby (UWA) 
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There will be refreshments in Maths & Stats tea room at 15:40, and we will
go for drinks at the UWA Tavern or the UniClub after the seminar. All are most welcome.
Speaker: Stephen Glasby (University of Western Australia)
Title: Norman involutions and tensor products of unipotent Jordan blocks
Time and place: 16:00 Friday 17/11/2017 in Weatherburn LT
Abstract: Suppose R is an rxr unipotent matrix over some field F, i.e. its characteristic polynomial is (t1)^r. The Jordan form of R is a sum of unipotent Jordan blocks, so we obtain some partition of r. If S is a unipotent sxs matrix over F, then so is R times S. To understand the partition of rs afforded by R times S it suffices to understand the partition afforded by J_r times J_s where J_r denotes a single rxr unipotent Jordan block. When char(F)=p, we denote this partition by lambda(r,s,p).
When p>0, the partitions lambda(r,s,p) are shrouded in mystery. Assume r<= s. We show that there is a larger set of 2^{r1}1 partitions (which is independent of p) and contains the mysterious partitions. These partitions correspond to involutions in the symmetric group S_r of degree r, and also to nonempty subsets of the set {1,2,...,r1}. We also show that the group G(r,p)=<lambda(r,s,p)  s>= r>, is a wreath product, and we determine its structure.
One motivation for this research comes from representation theory: understanding the structure of the Green ring. This is joint work with Cheryl E. Praeger and Binzhou Xia.
Contact 
Stephen Glasby
<glasbys@gmail.com>

Start 
Fri, 17 Nov 2017 16:00

End 
Fri, 17 Nov 2017 17:00

Submitted by 
Stephen Glasby <glasbys@gmail.com>

Last Updated 
Mon, 13 Nov 2017 20:13

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