Motivic Springer theory

2021 ◽  
Author(s):  
Jens Niklas Eberhardt ◽  
Catharina Stroppel
Keyword(s):  
Springer Theory

scholarly journals Springer theory in braid groups and the Birman–Ko–Lee monoid

2002 ◽  
Vol 205 (2) ◽  
pp. 287-309 ◽  
Author(s):  
David Bessis ◽  
François Digne ◽  
Jean Michel
Keyword(s):  
Braid Groups ◽  
Springer Theory

scholarly journals Langlands duality and global Springer theory

2012 ◽  
Vol 148 (3) ◽  
pp. 835-867 ◽  
Author(s):  
Zhiwei Yun
Keyword(s):  
Chern Class ◽  
Class Action ◽  
Dual Group ◽  
The Other ◽  
Support Theorem ◽  
Langlands Duality ◽  
Dual Groups ◽  
Geometric Langlands ◽  
Springer Theory ◽  
Singular Fibers

AbstractWe compare the cohomology of (parabolic) Hitchin fibers for Langlands dual groups G and G∨. The comparison theorem fits in the framework of the global Springer theory developed by the author. We prove that the stable parts of the parabolic Hitchin complexes for Langlands dual group are naturally isomorphic after passing to the associated graded of the perverse filtration. Moreover, this isomorphism intertwines the global Springer action on one hand and Chern class action on the other. Our result is inspired by the mirror symmetric viewpoint of geometric Langlands duality. Compared to the pioneer work in this subject by T. Hausel and M. Thaddeus, R. Donagi and T. Pantev, and N. Hitchin, our result is valid for more general singular fibers. The proof relies on a variant of Ngô’s support theorem, which is a key point in the proof of the Fundamental Lemma.

scholarly journals Springer theory via the Hitchin fibration

2011 ◽  
Vol 147 (5) ◽  
pp. 1635-1670 ◽  
Author(s):  
David Nadler
Keyword(s):  
Fukaya Category ◽  
Group Representations ◽  
Langlands Program ◽  
Geometric Langlands Program ◽  
Constructible Sheaves ◽  
Geometric Langlands ◽  
Springer Theory ◽  
Hitchin Fibration ◽  
Semisimple Complex ◽  
The Fourier Transform

AbstractWe develop the Springer theory of Weyl group representations in the language of symplectic topology. Given a semisimple complex group G, we describe a Lagrangian brane in the cotangent bundle of the adjoint quotient 𝔤/G that produces the perverse sheaves of Springer theory. The main technical tool is an analysis of the Fourier transform for constructible sheaves from the perspective of the Fukaya category. Our results can be viewed as a toy model of the quantization of Hitchin fibers in the geometric Langlands program.

scholarly journals Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory

2018 ◽  
Vol 292 (3-4) ◽  
pp. 1387-1430 ◽  
Author(s):  
Catharina Stroppel ◽  
Arik Wilbert
Keyword(s):  
Springer Theory ◽  
Springer Fibers
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