Representation rings for fusion systems and dimension functions
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Author(s)
Yalçın, Ergün
Reeh, Sune Nikolaj Precht
Date Issued
May 2017
Journal
Mathematische Zeitschrift
Publisher
Springer Berlin Heidelberg
Citation
Reeh, Sune Precht, and Ergün Yalçın. “Representation Rings for Fusion Systems and Dimension Functions.” Mathematische Zeitschrift, vol. 288, no. 1–2, Feb. 2018, pp. 509–30.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00209-017-1898-8
