Examines absolutely indecomposable quasi-parabolic G-bundles on P^1 and provides a geometric interpretation of character tensor multiplicities for finite reductive groups via generic additive character varieties.
Higgs bundles and indecomposable parabolic bundles over the projective line
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abstract
In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological interpretation for this counting using the moduli space of Higgs fields on the given vector bundle over the complex projective line with prescribed residues. We prove a certain number of results which bring evidences to the main conjecture. We detail the case of rank 2 vector bundles.
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2026 1verdicts
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Absolutely indecomposable quasi-parabolic $G$-bundles and the multiplicity of irreducible characters
Examines absolutely indecomposable quasi-parabolic G-bundles on P^1 and provides a geometric interpretation of character tensor multiplicities for finite reductive groups via generic additive character varieties.