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Quiver varieties and the character ring of general linear groups over finite fields

Emmanuel Letellier (2013)

Journal of the European Mathematical Society

Given a tuple ( 𝒳 1 , ... , 𝒳 k ) of irreducible characters of G L n ( F q ) we define a star-shaped quiver Γ together with a dimension vector v . Assume that ( 𝒳 1 , ... , 𝒳 k ) is generic. Our first result is a formula which expresses the multiplicity of the trivial character in the tensor product 𝒳 1 𝒳 k as the trace of the action of some Weyl group on the intersection cohomology of some (non-affine) quiver varieties associated to ( Γ , v ) . The existence of such a quiver variety is subject to some condition. Assuming that this condition is satisfied, we...

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