An Invitation to the Representation Theory of Finite Groups

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Programme

The proposed programme for the meeting is as follows.

09:30 - 10:30 Radha Kessar
10:30 - 11:30 Coffee Break
11:30 - 12:30 Gabriel Navarro
12:30 - 14:00 Lunch
14:00 - 15:00 Gunter Malle
15:00 - 15:30 Break
15:30 - 16:30 Meinolf Geck

Please note that all talks will take place in room 1BC45 on the first floor of the the maths department building Torre Archimede, Via Trieste 63, 35121 Padova.

Titles and Abstracts

Meinolf Geck - On the construction of semisimple Lie algebras and Chevalley groups

Abstract: The theory of canonical bases of quantum groups shows that simple modules for Lie algebras admit bases with very favourable properties. In this talk we explain a recent observation of Lusztig concerning the canonical basis of the adjoint representation which leads to a simplified construction of semisimple Lie algebras and Chevalley groups.

Radha Kessar - On scalar symmetric algebras and virtually irreducible lattices.

Abstract: A fundamental property of finite group algebras is that they are symmetric. To every symmetric algebra (projective and of finite rank as a module over the base ring) is associated a distinguished set of central elements of the algebra, called the central Casimir elements. If a symmetric algebra has a central Casimir element which is a scalar multiple of the identity the algebra is called a scalar symmetric algebra. Examples of scalar symmetric algebras include finite group algebras, blocks, source algebras, and some Hopf algebras. However, there exist symmetric algebras with the property that no algebra in their Morita equivalence class is scalar symmetric. In my talk, I will explain how many concepts from the modular representation theory of finite groups can be carried over to the more general setting of scalar symmetric algebras, in particular that of virtually irreducible lattices. The key ingredient is the special form taken by Tate duality in the context of scalar symmetric algebras. This is joint work with Florian Eisele, Michael Geline, and Markus Linckelmann.

Gunter Malle - Counting characters of finite groups

Abstract: How many irreducible representations does a finite group have? In this talk we will discuss various versions of this problem, present some conjectures, give partial answers and outline many open questions.

Gabriel Navarro - Character Tables and Sylow Subgroups

Abstract: Let G be a finite group. The character values of G give information on the local structure of a finite group and vice-versa.

Last Updated: 31/03/2016