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Suppose we have an G-equivariant sheav $\mathcal F$ on a smooth variety $X$. Can we split $\mathcal F$ as sum of eigensheaves? (I have seen this for structure sheaf but not sure if we can do it for any G-equivariant sheaf). Any reference please.

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    $\begingroup$ What is $G$, and what do you call an eigensheaf? $\endgroup$
    – abx
    Oct 3, 2015 at 19:10
  • $\begingroup$ G is any finite group. For eigensheaves please see equation 5 on page 2 of the following paper: citeseerx.ist.psu.edu/viewdoc/… $\endgroup$
    – A G
    Oct 3, 2015 at 19:31
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    $\begingroup$ That paper is about abelian groups. Is your group abelian? $\endgroup$
    – abx
    Oct 3, 2015 at 20:10
  • $\begingroup$ My group is Abelian. But is it true for non-Abelian groups? $\endgroup$
    – A G
    Oct 4, 2015 at 7:04
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    $\begingroup$ Of course not, already when $X$ is a point. When you ask a question here, try to describe precisely the problem you are considering. For instance, does $G$ act on $X$? $\endgroup$
    – abx
    Oct 4, 2015 at 7:32

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