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Mathematics > Representation Theory

arXiv:1805.06514 (math)
[Submitted on 16 May 2018 (v1), last revised 13 Nov 2023 (this version, v2)]

Title:Affine Matsuki correspondence for sheaves

Authors:Tsao-Hsien Chen, David Nadler
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Abstract:We lift the affine Matsuki correspondence between real and symmetric loop group orbits in affine Grassmannians to an equivalence of derived categories of sheaves. In analogy with the finite-dimensional setting, our arguments depend upon the Morse theory of energy functions obtained from symmetrizations of coadjoint orbits. The additional fusion structures of the affine setting lead to further equivalences with Schubert constructible derived categories of sheaves on real affine Grassmannians.
Comments: Add a new section (Section 9) on compatibility with Hecke actions
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG)
Cite as: arXiv:1805.06514 [math.RT]
  (or arXiv:1805.06514v2 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1805.06514

Submission history

From: Tsao-Hsien Chen [view email]
[v1] Wed, 16 May 2018 20:35:59 UTC (47 KB)
[v2] Mon, 13 Nov 2023 16:00:35 UTC (50 KB)
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