Perverse sheaves on real loop Grassmannians

By D. Nadler. 2002

50 citations recorded by the source corpus.

The aim of this paper is to identify a certain tensor category of perverse sheaves on the loop Grassmannian Grℝ of a real form Gℝ of a connected reductive complex algebraic group G with the category of finite-dimensional representations of a connected reductive complex algebraic subgroup $\check{H}$ of the dual group $\check{G}$. The root system of $\check{H}$ is closely related to the restricted root system of Gℝ. The fact that $\check{H}$ is reductive implies that an interesting family of real algebraic maps satisfies the conclusion of the Decomposition Theorem of Beilinson-Bernstein-Deligne.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eb0fed9b6524d0d48800631fb560b0aa59e34a24

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In Geometry and Topology

1. E. Witten
2. David Ben-Zvi
3. D. Gaiotto
4. D. Nadler
5. M. A. Cataldo
6. L. Migliorini
7. Xinwen Zhu
8. D. Gaitsgory

In Mathematical Physics

1. E. Witten
2. D. Nadler
3. D. Gaiotto
4. David Ben-Zvi
5. M. A. Cataldo
6. L. Migliorini
7. D. Gaitsgory
8. Xinwen Zhu

Citations in the corpus

• S-duality of boundary conditions in N=4 super Yang-Mills theory (2008, methodology): “Our table can be compared to the first three lines in Table 1 of [41], which refer to the group An−1 = SU(n).”
• The decomposition theorem, perverse sheaves and the topology of algebraic maps (2007, background): “10 Nadler investigated ([148]) a subcategory of perverse sheaves on the affine Grassmannian of a real form GR of G and proved that it is equivalent to the category of representations of a reductive subgroup LH of LG.”
• The Geometric Satake Correspondence for Ramified Groups (2011, result): “(iii) Our theorem and the method also share the similar features with the results of Nadler on geometric Satake for real groups [20].”
• Spherical varieties and Langlands duality (2006, background): “that associated to the corresponding real group in [ Nad05 ].”
• Betti Geometric Langlands (2016, background): “stack of α-twisted Y -parabolic GL local systems on X. In the case where X(R) is nonempty, one should take into account the additional structure to the Hecke modifications along real points studied in [N1], and given a string theory interpretation in [GW, Section 6]. Let us focus on the special case ”