Clifford Algebras, Spin Groups and Spinor Representations

This talk is part of the following reading seminar: Seiberg-Witten theory (Fall 2025).

Abstract

In this talk we will set the linear algebra preliminaries for the formulation of the Seiberg–Witten equations. These include Clifford algebras, Spin and Spin^c groups and spinor representations. Although the theory can be presented in great generality, for the sake of clarity we will often restrict to the case of interest for us: that of positive definite metrics on even-dimensional vector spaces.