We define the representation ring of a saturated fusion system $$\mathcal F$$ F as the Grothendieck ring of the semiring of $$\mathcal F$$ F -stable representations, and study the dimension functions of $$\mathcal F$$ F -stable representations using the transfer map induced by the characteristic idempotent of $$\mathcal F$$ F . We find a list of conditions for an $$\mathcal F$$ F -stable super class function to be realized as the dimension function of an $$\mathcal F$$ F -stable virtual representation. We also give an application of our results to constructions of finite group actions on homotopy spheres.
Mathematische Zeitschrift – Springer Journals
Published: May 10, 2017
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