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arXiv · 2101.01913

Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications

Xueqing Wen
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Abstract

We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on $\mathbb{P}^1$ and the quiver variety associated to a star-shaped quiver. As applications, we deduce a closed formula for the Littlewood-Richardson coefficients from the Verlinde formula, and solve the nilpotent case of the Deligne-Simpson problem via geometric methods.

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Xueqing Wen. 2021-01-06. Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications. https://arxiv.org/abs/2101.01913

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