Spherical varieties and Langlands duality
By D. Gaitsgory, D. Nadler, P. Deligne. 2006
51 citations recorded by the source corpus.
Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought of as an algebraic model for the loop space of X. In this paper, we associate to X a connected reductive complex algebraic subgroup $\check H$ of the dual group $\check G$. The construction of $\check H$ is via Tannakian formalism: we identify a certain tensor category Q(Z) of perverse sheaves on Z with the category of finite-dimensional representations of $\check H$. Combinatorial shadows of the group $\check H$ govern many aspects of the geometry of X such as its compactifications and invariant differential operators. When X is a symmetric variety, the group $\check H$ coincides with that associated to the corresponding real form of G via the (real) geometric Satake correspondence.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e74617b7dfc037d539dd3c7581d03c1889bd8de7
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Spherical varieties and integral representations of L-functions (2009, methodology): “2Notice that this is different from that of [Gaitsgory and Nadler 2010], but compatible with the notation used in [Sakellaridis 2008; 2009; Sakellaridis and Venkatesh 2012].”
- Spherical functions on spherical varieties (2009, methodology): “alizesthe Iwasawa(for X = U\G) and Cartan(for X = G′, G = G′ ×G′) decompositions. It was proven by Luna and Vust [LV83] in the case o = C[[t]]. An alternate proof was given by Gaitsgory and Nadler in [GN10], which was adapted to the p-adic case, under assumptions which hold at almost every place if ”