Semiorthogonal decomposition of $\mathrm{D}^b(\mathrm{Bun}_2^L)$

Abstract: We study the derived category of coherent sheaves on various versions of moduli space of vector bundles on curves by the Borel-Weil-Bott theory for loop groups and $\Theta$-stratification, and construct a semiorthogonal decomposition with blocks given by symmetric powers of the curve.