Ruhr-Universität Bochum
Fakultät für Mathematik
Universitätsstrasse 150
D-44780 Bochum
NA 2/33
Tel.: +49 (0)234/32-28304
Fax: +49 (0)234/32-14025
eMail: gerhard.roehrle@rub.de
Sprechstunde:
dienstags, 11 - 12 Uhr
und nach Vereinbarung
Arbeitsgebiete
- Algebraische Lie Theorie
- Algebraische Gruppen
- Darstellungstheorie
- DFG project: Serre's notion of Complete Reducibility and Geometric Invariant Theory (within the
DFG Priority Programme in Representation Theory).
- DFG project: Computational aspects of the Cohomology of Coxeter arrangements: On Conjectures of Lehrer-Solomon and Felder-Veselov (within the
DFG Priority Programme "Algorithmic and experimental methods in Algebra,
Geometry and Number Theory").
- Publications on
MathSciNet.
- Recent preprints on the
ArXiv.
- Latest preprints:
G-complete reducibility in non-connected groups
with M. Bate, S. Herpel and B. Martin
Abstract:
In this paper we present an algorithm for determining whether a subgroup H of a non-connected reductive group G is G-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, such as checking whether a certain subgroup of G^0 is G^0 -cr. This essentially reduces the problem of determining G-complete reducibility to the connected case.
math.GR/1303.0963
Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and seven
with S. M. Goodwin and P. Mosch
Abstract:
Let G(q) be a finite Chevalley group, where q is a power of a good prime p, and let U(q) be a Sylow p-subgroup of G(q). Then a generalized version of a conjecture of Higman asserts that the number k(U(q)) of conjugacy classes in U(q) is given by a polynomial in q with integer coefficients. In an earlier paper, the first and the third authors developed an algorithm to calculate the values of k(U(q)). By implementing it into a computer program using GAP, they were able to calculate k(U(q)) for G of rank at most 5, thereby proving that for these cases k(U(q)) is given by a polynomial in q. In this paper we present some refinements and improvements of the algorithm that allow us to calculate the values of k(U(q)) for finite Chevalley groups of rank six and seven, except E_7. We observe that k(U(q)) is a polynomial, so that the generalized Higman conjecture holds for these groups. Moreover, if we write k(U(q)) as a polynomial in q-1, then the coefficients are non-negative. Under the assumption that k(U(q)) is a polynomial in q-1, we also give an explicit formula for the coefficients of k(U(q)) of degrees zero, one and two.
math.GR/1302.6904
Equivariant K-theory of generalized Steinberg varieties
with J. M. Douglass
Abstract:
We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its nilpotent cone in terms of the extended affine Hecke algebra and double cosets in the extended affine Weyl group. As an application, we use this description to define Kazhdan-Lusztig "bar" involutions and Kazhdan-Lusztig bases for these equivariant K-groups.
math.RT/1302.4530
Former and current PhD students:
Simon Goodwin
(University of Birmingham)
Michael Bate
(University of York)
Russell Fowler (Npower)
Glenn Ubly (NHS)
Sebastian Herpel (University of Kaiserslautern)
Peter Mosch
Nils Amend
Editorial Activity:
Tbilisi Mathematical Journal
.
Computer Programs

