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We calculate the dg algebra of global functions on commuting stacks ofcomplex reductive groups using tools from Betti Geometric Langlands. Inparticular, we prove that the ring of invariant functions on the commutingscheme is reduced. Our main technical results include: a semi-orthogonaldecomposition of the cocenter of the affine Hecke category; and the calculationof endomorphisms of a Whittaker sheaf in a diagram organizing parabolicinduction of character sheaves.

Functions on the commuting stack via Langlands duality