SEMINAR: Groups and Combinatorics Seminars


Groups and Combinatorics Seminars
Eric Swartz (Binghamton)
will speak on
Locally 2arc transitive graphs admitting an almost simple group of Suzuki type
at 3pm in MLR2
and
Jan Saxl (Cambridge)
will speak on
Conjugation characters of simple groups
at 4pm in MLR2
Abstract 1:
A graph Gamma is said to be locally (G,2)arc transitive for G a subgroup of Aut(Gamma) if Gamma contains a 2arc, and, for any vertex alpha of Gamma, G is transitive on the 2arcs of Gamma starting at alpha. In this talk, we will discuss general results involving locally (G,2)arc transitive graphs and recent progress toward the classification of the locally (G,2)arc transitive graphs, where G is a subgroup of Aut(Sz(q)) with soc(G) = Sz(q), q = 2^m for some odd natural number m. In particular, we will discuss seven families of vertexintransitive locally (G,2)arc transitive graphs. Furthermore, for any graph Gamma in one of these families, the full automorphism group of Gamma is a subgroup of Aut(Sz(q)), and the only locally 2arc transitive graphs admitting an almost simple group of Suzuki type whose vertices all have valency at least three are (i) graphs in these seven families, (ii) (vertex transitive) 2arc transitive graphs admitting an almost simple group of Suzuki type, or (iii) double covers of the graphs in (ii). Since the graphs in (ii) have been classified by Fang and Praeger (``Finite twoarc transitive graphs admitting a Suzuki simple group," Comm. Alg., 27(8):37273754, 1999), this completes the classification of locally 2arc transitive graphs admitting a Suzuki simple group.
Abstract 2:
In this talk we consider two problems concerning ordinary
representations of simple groups: characters of conjugation actions,
and squares of irreducible characters. These turn out to be closely
related. This is joint work with Heide, A. Zalesskii, and Tiep.
Speaker(s) 
Eric Swartz and Jan Saxl


Contact 
Michael Giudici
<[email protected]>

Start 
Wed, 25 Jan 2012 15:00

End 
Wed, 25 Jan 2012 17:00

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Tue, 24 Jan 2012 12:03

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