Orthosymplectic Satake equivalence

Abstract

This is a companion paper of arXiv:1909.11492. We prove an equivalence relating representations of a degenerate orthosymplectic supergroup with the category of $SO(N-1,\mathbb{C}[[t]])$-equivariant perverse sheaves on the affine Grassmannian of $S{O}_N$. We explain how this equivalence fits into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.

v2: 31 pages, a few minor corrections; Conjecture 3.3.4 became Theorem 3.3.5. v3: 32 pages, proof of Lemma 2.3.3 corrected. v4: minor corrections. v5: the final published version

Cited by in corpus (4)

• Moment map and matrix integrals
• Hyperspherical equivariant slices and basic classical Lie superalgebras
• Duality via convolution of W-algebras
• Resolution of singularities of the odd nilpotent cone of orthosymplectic Lie superalgebras