Real Representations of $C_2$-Graded Groups: The Antilinear Theory

Dmitriy Rumynin; James Taylor

Real Representations of $C_2$-Graded Groups: The Antilinear Theory

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arxiv 2006.09765 v4 pith:TYIAUPJI submitted 2020-06-17 math.RT math.GRmath.RA

Dmitriy Rumynin , James Taylor This is my paper · ORCID

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keywords gradedantilineartheoryfinitegrouprepresentationsactsgroups

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abstract

We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite $C_2$-graded groups. A finite $C_2$-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial component of the theory. Among other things, we study characters and Frobenius-Schur indicators. As an example, we describe the antilinear representations of the $C_2$-graded group $A_n \leq S_n$.

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A family completion theorem for tempered cohomology
math.AT 2026-08 accept novelty 7.0 of 10

For oriented P-divisible groups over noetherian E-infinity rings, family-completion of tempered cohomology modules is equivalent to algebraic completion at the corresponding ideal, generalizing Atiyah–Segal and AHJM.

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