Algebra Workshop

All talks in Rutherford Theatre - Schuster Building

15:30 Scott Harper
University of St Andrews
How big can a minimal generating set be?
A generating set for a group is said to be minimal if no proper subset generates the group. A minimal generating set need not have minimum possible size. For example, the symmetric group of degree n has a generating set of size two, but the set { (1, 2), (2, 3), ..., (n-1, n) } of n-1 adjacent transpositions is also a minimal generating set. In this talk, I will discuss recent work that provides an upper bound on the maximal size of a minimal generating set for an arbitrary finite group, which settles a conjecture of Lucchini, Moscatiello and Spiga. The proof of this result involves a connection with bases for primitive permutation groups.

16:10 Stacey Law
University of Birmingham
Sylow restriction in the representation theory of finite groups
One of the central themes in the representation theory of finite groups is to understand the relationship between the characters of a finite group G and those of its local subgroups. Following an overview of some of the recent major developments in this area, we will then focus on Sylow branching coefficients. These were introduced to describe the restriction of irreducible characters of G to a Sylow subgroup P of G, and have been recently shown to characterise structural properties such as the normality of P in G. We will also discuss and present some new results on Sylow branching coefficients for symmetric groups.

16:50 Adam Thomas
University of Warwick
sl2, fake sl2 and pgl2 subalgebras
Let g be the Lie algebra of a simple algebraic group over an algebraically closed field of characteristic p. When p=0 the celebrated Jacobson-Morozov Theorem promises that every non-zero nilpotent element of g is contained in an sl2 subalgebra. This has been extended to odd primes but what about p=2? There is a 3-dimensional simple Lie algebra, known colloquially as fake sl2, as well as sl2 and pgl2. In this talk we will discuss recent joint work with David Stewart determining which nilpotent elements of g have overalgebras isomorphic to one of these three Lie algebras.

11:30 Amit Hazi
University of Leeds
Quiver presentations and isomorphisms of Hecke categories and Khovanov arc algebras
The extended Khovanov arc algebras give a diagrammatic presentation of the principal block of parabolic category O in type (A_n, A_{k-1} x A_{n-k}). These algebras form a tower of basic, Koszul, quasi-hereditary algebras. In this talk I will discuss a new isomorphism of these algebras with the (basic) endomorphism algebras in the anti-spherical Hecke category, which gives rise to a presentation by quiver and relations. This talk is based on joint work with Chris Bowman, Maud De Visscher, and Catharina Stroppel.

13:45 Martina Balagović
University of Newcastle
Towards bases for representations of QSP coideal subalgebras
I will discuss an ongoing project on representations of certain quantum symmetric pair coideal subalgebras of quantum groups. By recent work of Stefan Kolb and Jake Stephens, such algebras have equivalents of roots, satisfy the PBW theorem, and their irreducible finite dimensional representations have weights and can be classified in terms of weights. We would now like to construct bases for these representations compatible with their relationship with quantum groups.

I will explain what are these algebras, why they are of interest, how they relate to quantum groups, and what Kolb and Stephens can show about their representations. I will then describe desired properties of the bases of these representations that one could hope for in analogy with classical Lie theory, list questions about structures which control these bases, and partially answer some of these questions. Joint work in progress with Stefan Kolb.

14:25 Dan Ciubotaru
University of Oxford
Bounds for the Langlands parameter of a smooth representation
In joint work with Ju-Lee Kim, we propose a bound for the Langlands parameter of a smooth irreducible representation of the reductive p-adic group in terms of the geometric wavefront set of the representation, an invariant that appears naturally in the local character expansion of Howe and Harish-Chandra. In the talk, I will concentrate in particular on the case of depth-zero representations where the bound is closely related to the Kawanaka wavefront set of the representations of finite reductive groups.

11:30 Rosemary Bailey
University of St Andrews
Latin squares in higher dimensions

11:50 Mikko Korhonen
SUSTech
Maximal Solvable Subgroups

12:10 Dmitry Kudryavtsev
University Manchester
Lengths of Tsetlin library algebras

14:00 Justin McInroy
University of Chester
Automorphisms of axial algebras

14:20 Abhiram Natarajan
Warwick
TBA

14:40 Zain Ahmed Kapadia
Queen Mary
On the Submodule Structure of Hook Specht Modules in Characteristic 2