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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Representation theory of diagram algebras - Oliver
King\, Leeds University
DTSTART;TZID=Europe/London:20141022T163000
DTEND;TZID=Europe/London:20141022T173000
UID:TALK55412AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/55412
DESCRIPTION:A diagram algebra is an algebra whose elements can
be represented as linear combinations of diagrams
. There are several common features of such algebr
as\, allowing us to use similar methods in analysi
ng their representation theory and obtaining simil
ar results. In this talk I will focus on the Braue
r and partition algebras\, introduced by Brauer an
d Martin respectively. The representation theory o
f both of these over a field of characteristic zer
o is well understood. I will recall the definition
s and give the block structure of both algebras in
characteristic zero in terms of the action of a r
eflection group on the set of simple modules. I wi
ll then give a description of the blocks in positi
ve characteristic by using the corresponding affin
e reflection group (for the partition algebra\, th
is is joint work with C. Bowman and M. De Visscher
). Finally I will show that by restricting our att
ention to specific families of these algebras\, we
can in fact obtain the entire decomposition matri
x.\n
LOCATION:MR12
CONTACT:David Stewart
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