Algebra and Geometry Seminar: Sune Precht Reeh

Thursday 13 December 2018, 2:00pm to 3:00pm

Venue

PSC A54 LT - View Map

Open to

Postgraduates, Staff, Undergraduates

Registration

Registration not required - just turn up

Event Details

Representation rings for fusion systems and dimension functions

Given a representation V of a finite group G we can associate a dimension function that to each subgroup H of G assigns the dimension of the fixed point space VH. The dimension functions are "super class functions" that are constant on the conjugacy classes of subgroups in G. For a p-group the list of Borel-Smith conditions characterizes the super class functions that come from real representations. In a joint project with Ergün Yalcin we show that while we cannot lift Borel-Smith functions to real representations for a general group G, we can lift a multiple of any Borel-Smith function to an action of G on a finite homotopy sphere (which would be the unit sphere if we had a representation). To prove this we localize at each prime p and study dimension functions for saturated fusion systems. That is, we give a list of Borel-Smith conditions for a fusion system that characterize the dimension functions of the fusion stable real representations. The proof for fusion systems involves biset functors for saturated fusion systems.

Contact Details

Name Łukasz Grabowski
Email

lukasz.grabowski@lancaster.ac.uk

Telephone number

+44 (0)1524 593444