Kac-type conjecture for the spherical Hall Lie algebra

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Let Ag,r,d(0)A_{g,r,d}(0) be the constant term of the polynomial counting absolutely indecomposable vector bundles of rank rr and degree dd, and let hsph\mathfrak{h}^{\mathrm{sph}} be the spherical Hall Lie algebra with graded component h(r,d)sph\mathfrak{h}^{\mathrm{sph}}_{(r,d)}. Kac-type conjecture. For every (r,d)∈(Z2)+(r,d)\in(\mathbb{Z}^2)^+,

Ag,r,d(0)=dimh(r,d)sph.A_{g,r,d}(0)=\text{dim}\mathfrak{h}^{\mathrm{sph}}_{(r,d)}.

This is proposed as the analogue for curves of Kac's conjecture identifying constant terms of Kac polynomials with root multiplicities. The source gives no resolution.

References

Primary source

Olivier Schiffmann, “Indecomposable vector bundles and stable Higgs bundles over smooth projective curves”, arXiv:1406.3839 (2014).

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