Date
Fri, 20 Nov 2020
Time
14:00 - 15:00
Location
Virtual
Speaker
James Taylor
Organisation
University of Oxford

A Real representation of a $C_2$-graded group $H < G$ ($H$ an index two subgroup) is a complex representation of $H$ with an action of the other coset $G \backslash H$ (“odd" elements) satisfying appropriate algebraic coherence conditions. In this talk I will present three such Real representation theories. In these, each odd element acts as an antilinear operator, a bilinear form or a sesquilinear form (equivalently a linear map to $V$ from the conjugate, the dual, or the conjugate dual of $V$) respectively. I will describe how these theories are related, how representations in each are classified, and how the first generalises the classical representation theory of $H$ over the real numbers - retaining much of its beauty and subtlety.

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