Combinatorial decomposition theorem for Hitchin systems via zonotopes

Abstract

We determine the summands of the decomposition theorem for the Hitchin system for ${\mathrm{GL}}_n$, in arbitrary degree, over the locus of reduced spectral curves. The key ingredient is an equivariant formula for lattice point counts in graphical zonotopes.

49 pages. 7 figures. 2 tables. Final version to appear at Crelle