researchseminars.org

Jeffrey Adams (University of Maryland)
2022-08-18 14:30 - 16:00 UTC | https://researchseminars.org/talk/atlas/33/
Title: Hermitian forms on finite- dimensional representations (https://researchseminars.org/talk/atlas/33/)
by Jeffrey Adams (University of Maryland) as part of Real reductive groups/atlas

Abstract
The study of signatures of Hermitian forms on finite dimensional representations serves as an example of the general theory, while having some special features, and being surprisingly interesting in its own right.

The finite dimensional representations of the real forms $G(\mathbb R)$ of $G(\mathbb C$) are essentially independent of the real form. However these representations are all unitary if and only if $G(\mathbb R)$ is compact, and the signature of the Hermitian forms depend very much on the real form.

We'll talk about computing this, using an elementary formula (arising from the Atlas theory of the c-form)in terms of the Weyl character formula. We'll also discuss some interesting invariants for a finite dimensional representation: the Frobenius/Schur indicator and the real-quaternionic indicator.
