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math.RT2025
Tame local Betti geometric Langlands
Gurbir Dhillon, Jeremy Taylor
We prove a monoidal equivalence between spectral and automorphic realizations of the universal affine Hecke category, thereby proving the tamely ramified local Betti geometric Lang…
math.RT2025
The universal monodromic Arkhipov--Bezrukavnikov equivalence
Gurbir Dhillon, Jeremy Taylor
We identify equivariant quasicoherent sheaves on the Grothendieck alteration of a reductive group with universal monodromic Iwahori--Whittaker sheaves on the enhanced…
math.RT2024
The real affine Grassmannian and quantum SL(2)
Mark Macerato, Jeremy Taylor
We prove that the category of equivariant perverse sheaves on the affine Grassmannian of PGL(2, R) is highest weight and we construct the projective objects. Moreover we prove that…