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arXiv · 2408.00931

The real affine Grassmannian and quantum SL(2)

Mark Macerato·Jeremy Taylor
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Abstract

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 the category of perverse sheaves on the odd component is equivalent to the principal block of Lusztig's quantum SL(2) at a primitive fourth root of unity.

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Mark Macerato, Jeremy Taylor. 2024-08-01. The real affine Grassmannian and quantum SL(2). https://arxiv.org/abs/2408.00931

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