Algebra Seminar: Dipper -- Unipotent Specht modules of finite general linear groups and some conjectures of Higman, Lehrer and Isaacs

There will be an algebra seminar on Friday 25 November, given by Richard Dipper.  Note
the unusual room.  

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Speaker: Richard Dipper (University of Stuttgart) 

Date: Friday 25 November 

Time: 12:05-12:55pm 

Venue: Carslaw 273 

Title: 

Unipotent Specht modules of finite general linear groups and some conjectures of Higman,
Lehrer and Isaacs 

Abstract: 

Let G=GL(n,q), q some prime power, and let U be the subgroup of unipotent lower
triangular matrices of G.  We determine the precise U-module structure of the unipotent
Specht type modules of G associated with two part partitions over finite fields of
characteristic not dividing q.  This provides a new construction and a
representation-theoretic interpretation for the standard basis of these modules which
was obtained by Brandt, James, Lyle and myself in previous work.  It is conceivable that
this construction is accessible to generalisation to arbitrary partitions of n.  It is
explained, how this new approach relates to longstanding conjectures of Higman, Lehrer
and a more recent one of Isaacs on the number of ordinary irreducible characters of U.  

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Anne Thomas - [email protected] 
Seminar website - http://www.maths.usyd.edu.au/u/AlgebraSeminar/