Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications
Abstract
We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on P1 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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