geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
In geometric representation theory the horocycle correspondence for a complex reductive group and a Borel subgroup is the correspondence of group quotients given by
This generalizes the Grothendieck-Springer correspondence. (Ben-Zvi & Nadler 09, example 1.2)
The pull-push integral transform of D-modules from right to left through this correspondence is the Harish-Chandra transform
from the Hecke category on the left.
A (unipotent) character sheaf? (Lusztig 85) for is a simple object-direct summand of a D-module that is in the image of a simple object under this transform. (Ginzburg 89)
Original articles include
George Lusztig, Character sheaves I. Adv. Math 56 (1985) no. 3, 193-237.
Victor Ginzburg, Admissible modules on a symmetric space. Orbites unipotentes et représentations, III. Astérisque No. 173-174 (1989), 9–10, 199–255.
Interpretation in the context of extended TQFT is in
Last revised on August 2, 2017 at 17:51:28. See the history of this page for a list of all contributions to it.