Algebra seminars, 2010-11

Algorithms and numbers of generators for finite matrix groups

Derek Holt, University of Warwick

Thursday 7 October 2010, 16:30-17:30
Watson Building, Lecture Room A

Abstract not available

On Behr's rank conjecture on the finiteness properties of S-arithmetic groups

Ralf Gramlich, University of Birmingham

Thursday 14 October 2010, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

The isomorphism problem for almost split Kac-Moody groups

Guntram Hainke, University of Birmingham

Thursday 14 October 2010, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

A refinement of the McKay conjecture for arbitrary finite groups

Anton Evseev, Queen Mary, University of London

Thursday 28 October 2010, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

TBA

Sergey Shpectorov, University of Birmingham

Wednesday 10 November 2010, 14:00-15:00
Watson Building, Lecture Room A

Abstract not available

TBA

Peter Rowley, University of Manchester

Wednesday 10 November 2010, 15:00-16:00
Watson Building, Lecture Room A

Abstract not available

TBA

Rob Wilson, Queen Mary, University of London

Wednesday 10 November 2010, 16:30-17:30
Watson Building, Lecture Room A

Abstract not available

Aspherical values of rational Cherednik algebras

Stephen Griffeth, University of Edinburgh

Thursday 18 November 2010, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

Modular Lie powers of relation modules and free central extensions of groups

Ralph Stohr, University of Manchester

Thursday 25 November 2010, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

Lie theory for finite simple groups

Shahn Majid, Queen Mary, University of London

Thursday 9 December 2010, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

Characteristic varieties of modules over enveloping algebras and Iwasawa algebras

Konstantin Ardakov, University of Nottingham

Thursday 16 December 2010, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

Irreducible actions of geometric subgroups of classical algebraic groups

Donna Testermann, EPFL

Thursday 10 February 2011, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

TBA

Martin Kassabov, University Southampton

Thursday 17 February 2011, 16:00-17:00
Watson Building, Lecture Room A

Abstract not available

Generalized spin representations

Guntram Hainke, University of Birmingham

Thursday 24 February 2011, 16:00-17:00
Watson Building, Lecture Room A

The special orthogonal group SOn(ℝ) is a maximal compact subgroup of SLn(ℝ). Its Lie algebra son(ℝ) is therefore called a maximal compact subalgebra of sln(ℝ), and it can be characterized as the fixed point set of the Cartan–Chevalley involution ω: A→−AT of sln(ℝ).

Kac–Moody algebras were introduced in the 1960s to generalize complex semisimple Lie algebras and have since then found applications in theoretical physics. For a Kac–Moody algebra g one can similarly define its maximal compact subalgebra as k = Fix ω.

In the case of g = E10(ℝ), theoretical physicists have discovered that the spin representation of so10(ℝ) = k(A9) ≤ k(E10) can be extended to a representation of k(E10).

In this talk, we discuss this representation and introduce a general framework which encompasses it. With the help of these so-called generalized spin representations, we derive some algebraic properties of maximal compact subalgebras of simply-laced Kac–Moody algebras.

This is joint work with Ralf Gramlich.

Finite groups of Lie type as Galois groups over rational numbers

Gordon Savin, University of Utah

Thursday 17 March 2011, 16:00-17:00
Watson Building, Lecture Room A

Let l be a rational prime. In a work with Khare and Larsen we proved that the groups of Lie type Bn, Cn and G2 over the finite field of order lk appear as Galois groups over rational numbers for infinitely many k. The main tool is l-adic representations attached to automorphic representations. Our approach consists of carefully constructing automorphic representations so that the corresponding l-adic representations give desired Galois groups.

Modules for elementary abelian groups and vector bundles on projective space

Dave Benson, University of Aberdeen

Wednesday 23 March 2011, 18:00-19:00
Watson Building, Lecture Room A

Abstract not available