Representation rings for fusion systems and dimension functions
We define the representation ring of a saturated fusion system F as the Grothendieck ring of the semiring of F-stable representations, and study the dimension functions of F-stable representations using the transfer map induced by the characteristic idempotent of F. We find a list of conditions for...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2018
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| Online Access: | http://hdl.handle.net/1721.1/114302 https://orcid.org/0000-0002-4913-8268 |
| Summary: | We define the representation ring of a saturated fusion system F as the Grothendieck ring of the semiring of F-stable representations, and study the dimension functions of F-stable representations using the transfer map induced by the characteristic idempotent of F. We find a list of conditions for an F-stable super class function to be realized as the dimension function of an F-stable virtual representation. We also give an application of our results to constructions of finite group actions on homotopy spheres. |
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