The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123
Gabriele Nebe (RWTH Aachen) - Orthogonal Representations of Finite Groups
10h30-11h30
16 December 2022
Gabriele Nebe (RWTH Aachen) - Orthogonal Representations of Finite Groups
Abstract: The character table of a finite group G lists invariants of the irreducible representations R:G\to GL_n(K). The first column gives the degree n. There is an additional column 0 containing the "indicator", a value in +, -, o telling you that R(G) is contained in an orthogonal, the symplectic or a unitary group in the respective cases.
In particular for finite fields K this gives all information about the classical group containing R(G) except for the case of even degree indicator +, where there are two non isomorphic orthogonal groups distinguished by the "orthogonal discriminant".
Together with Richard Parker and Thomas Breuer we computed the orthogonal discriminants for all finite simple groups in the ATLAS of finite groups up to the Harada Norton group.
The key point that made the computations feasible is to see the discriminant as the discriminant of an involution that allows to transfer well established condensation techniques to condensation of algebras with involution.
