# Algebra Seminar

### Seminars are held on Mondays at 17:00 in B3.02

#### Organisers: Adam Thomas and Gareth Tracey

(To see the abstract and title of a talk in the past, click on the speakers name to expand it)

#### Term 2:

**16th January:** *Scott Harper (St Andrews)*

**23rd January: ***Michael Bate (York)*

**30th January: **Miriam Norris (Manchester)

Title: Some composition multiplicities for tensor products of irreducible representations of GL(n).

Abstract: Understanding the composition factors of tensor products is an important question in representation theory. In characteristic 0 the classical Littlewood-Richardson coefficients describe the composition factors of both the tensor products of simple **C**GLn(**C**)-modules and the restriction of simple **C**GLn(**C**)-modules to some Levi subgroup.

Now let **F** denote an algebraically closed field of characteristic p > 0. In comparison very little is known about composition factors of tensor products of simple **F**GLn(**F**)-modules but it is thought that there may still be a relationship with the restriction of simple **F**GLn(**F**)-modules to some Levi subgroup. In this talk explore and explicit relationship of this kind for tensor products of simple **F**GLn(**F**)-modules with the wedge square of the dual natural module and see how this might be used to find composition factors.

**6th February: **Alastair Litterick (Essex)

Title: Representation varieties and rigidity in finite simple groups

Abstract: Building from the now-classical theorem that every non-abelian finite simple group is 2-generated, one can ask much more delicate questions, for instance on the abundance of generating pairs, or on the existence of generating pairs with particular orders, or from particular conjugacy classes.

For groups of Lie type, these questions can be studied using the representation variety Hom(F,G) where F is finitely generated and G is a reductive algebraic group. In work with Ben Martin (Aberdeen), we use the conjugation action of G on Hom(F,G) to interpret generators for groups of Lie type as certain Zariski-closed orbits. This allows us to prove and generalise a 2010 conjecture of C. Marion, and motivates this as an avenue in the wider study of generating sets in groups of Lie type.

**13th February: **Dylan Johnston (Warwick)

**20th February: **Nadia Mazza (Lancaster)

Postponed due to strike action**27th February: **Emily Norton (Kent)

**6th March (Online and broadcast in B3.02): **Attila Maróti (Alfréd Rényi Institute of Mathematics, Budapest)

**13th March: **Vanthana Ganeshalingham (Warwick)

#### Term 1:

**10th October: ** *Gareth Tracey (Warwick)*

**17th October: ***Kamilla Rekvényi (Imperial College London)*

**24th October: ***Alexandre Zalesski (UEA)*

**31st October: ***Sean Eberhard (Queen's University Belfast)*

**14th November: ***Jay Taylor (Manchester)*

**21st November: ***Diego Martin Duro (Warwick)*

**28th November: ***Rachel Pengelly (Birmingham)*

**5th December: ***Ana Retegan (Birmingham)*