# OIST Representation Theory Seminar

### Recordings of talks will be available on this page and here if the speaker agrees to have their talk recorded.

### Tuesday 10th October 2023, 4:30–5:30pm JST (UTC+9), online on Zoom

### Benjamin Sambale, Leibniz Universität Hannover

### Title: Groups of p-central type

**Abstract:** A finite group \(G\) with center \(Z\) is of central type if there exists an irreducible character \(\chi\) such that \(\chi(1)^2=|G:Z|\). Howlett–Isaacs have shown that such groups are solvable. A corresponding theorem for \(p\)-Brauer characters was proved by Navarro–Späth–Tiep under the assumption that \(p\ne 5\). I have shown that there are no exceptions for \(p=5\). Moreover, I give some applications to \(p\)-blocks with a unique Brauer character.

#### Meeting ID: 95084006503, password will be announced 24 hours before the talk.

### Tuesday 24th October 2023, 4:30–5:30pm JST (UTC+9), online on Zoom

### Emily Norton, University of Kent

### Title: TBA

**Abstract:** TBA

#### Meeting ID: 98775153562, password will be announced 24 hours before the talk.

### Tuesday 7th November 2023, 4:30–5:30pm JST (UTC+9), online on Zoom

### Ulrich Thiel, University of Kaiserslautern-Landau

### Title: The rank one property for free Frobenius extensions

**Abstract:** The Cartan matrix of a finite-dimensional algebra is the matrix of multiplicities of simple modules in indecomposable projective modules. This is crucial information about the representation theory of the algebra. In my talk I will present a general setting including several important examples from Lie theory, such as restricted quantized enveloping algebras at roots of unity, in which we could prove that the Cartan matrix has the remarkable property of being blockwise of rank one. This is joint work with Gwyn Bellamy.