Wed, 23 Oct 2013
11:30
11:30
Queen's College
Group word problems related to the context-free languages
Tara Brough
(St Andrews)
Abstract
The word problem of a group $G$ with respect to a generating
set $X$ is the set of all words in elements of $X$ and their inverses
which represent the identity in $G$. A formal language is a set of words over a finite alphabet, and so word problems of groups can be viewed as formal languages.
In this talk I will give an introduction to formal
languages, concentrating on context-free languages and several related
classes. I will define these languages by means of automata. I will
then give a survey of research on groups whose word problem belongs to
the language classes I have introduced, beginning with the
classification of groups with context-free word problem (Muller and
Schupp, 1983). I will also discuss some of the open problems in this
area.
Wed, 11 Nov 2009
11:30 -
12:30
ChCh, Tom Gate, Room 2
Tue, 10 Nov 2009
17:00 -
18:00
L2
Thu, 06 Nov 2008
14:30 -
15:30
L3
q-Schur algebras, Wedderburn decomposition and James' conjecture
Max Neunhoeffer
(St Andrews)
Abstract
In this talk we present a new construction of a Wedderburn basis for
the generic q-Schur algebra using the Du-Kazhdan-Lusztig basis. We show
that this gives rise to a new view on the Du-Lusztig homomorphism to the
asymptotic algebra. At the end we explain a potential plan for an attack
on James' conjecture using a reformulation by Meinolf Geck.
The talk starts with a gentle recollection of facts about
Iwahori-Hecke-Algebras of type A and q-Schur algebras and aims to be
accessible to people who are not (yet) experts in the representation
theory of q-Schur algebras.
All this is joint work with Olivier Brunat (Bochum).