Programm:
Tuesday 8th December:
14:00 -- 15:00: Schmidmeier. Invariant subspaces and their invariants.
15:00 -- 15:30: Coffee break
15:30 -- 16:15: Himstedt. Generic character tables of parabolic subgroups.
16:15 -- 17:00: Schneider. Representation theory of pointed Hopf algebras and
generalized quantum groups I
Wednesday 9th December:
09:00 -- 10:00: Jensen.
Generic orbits for the adjoint action of automorphism
groups of projective representations
10:00 -- 10:30: Coffee break
10:30 -- 11:15: Mikaelian. Generalised string modules and periodicity
11:15 -- 12:00: Schneider. Representation theory of pointed Hopf algebras and
generalized quantum groups II
(Afterwards: Lunch in the Mathematics and Computer Science Building)
Location: Lectures take place in the Department for Mathematics
and Computer Science, Boltzmannstrasse 3, Garching. On Tuesday the
first lecture takes place in Room 00.10.011; after the coffee break, the
lectures take place in Room 02.08.020. On Wednesday the lectures take
place in Room 00.10.011.
ABSTRACTS:
Generic orbits for the adjoint action of automorphism
groups of projective representations
(Jensen)
We study generic orbits for the adjoint action of an automorphism
group of a projective representation of a quiver without oriented cycles. In
particular, we consider the problem of deciding when there exists a
dense open orbit. We show that there exists a dense open orbit if and only
if the quiver is of Dynkin type.
Generalised string modules and periodicity
(Mikaelian)
We consider the \Omega-translates of the
p-permutation modules for Young subgroups of some S_n
over a field of charateristic $p$. These play an important
role in homology. After a discussion
of the general theory of the so called \Omega-periodic
$p$-permutation modules of a general finite group $G$ we
consider a case when those modules are not periodic. This
case is G=S_p\times S_p, and it turns out that in this
case the \Omega-translates of p-permutation modules
have particularly nice structural properties which we
describe in detail. This is done by giving a more general
construction, that of the Generalised String Modules.
Invariant subspaces and their invariants
(Schmidmeier)
Subspaces of vector spaces which are invariant under the
action of a linear operator have found a lot of interest since the
late 19th century: In the Jordan Normal Form Theorem, vector spaces
are decomposed as a direct sum of cyclic invariant subspaces. In
case the base field is finite, the invariant subspaces can be counted
(Steinitz, 1910; Hall, Green, Klein, 1968); one can try to classify
them up to isomorphy (hard) (Birkhoff, 1934), or study their
projective variety (Baer, 1942).
In my talk I want to discuss combinatorial isomorphism invariants
which are based on partitions. A particular role play the Klein
tableaux as they link the counting problem, the classification up to
isomorphy, and the geometric approch.
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