scholarly journals Local geometric Langlands correspondence: the spherical case

2019 ◽  
Author(s):  
Edward Frenkel ◽  
Dennis Gaitsgory
Keyword(s):  
Spherical Case ◽  
Langlands Correspondence ◽  
Geometric Langlands

scholarly journals On the Notion of Conductor in the Local Geometric Langlands Correspondence

2017 ◽  
Vol 69 (1) ◽  
pp. 107-129
Author(s):  
Masoud Kamgarpour
Keyword(s):  
Irreducible Representation ◽  
Galois Representation ◽  
Loop Group ◽  
Langlands Correspondence ◽  
Categorical Representation ◽  
Swan Conductor ◽  
Geometric Langlands ◽  
Meromorphic Connection ◽  
Local Langlands Correspondence ◽  
Geometric Analogue

AbstractUnder the local Langlands correspondence, the conductor of an irreducible representation of Gln(F) is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.

scholarly journals A Quantization Procedure of Fields Based on Geometric Langlands Correspondence

2009 ◽  
Vol 2009 ◽  
pp. 1-14
Author(s):  
Do Ngoc Diep
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Vector Bundles ◽  
Sigma Model ◽  
Fock Space ◽  
Loop Algebra ◽  
Target Space ◽  
Automorphic Representations ◽  
Langlands Correspondence ◽  
Geometric Langlands

We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry groupGL. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundles with connection over the space dual to the Lie algebra of the symmetry groupGL. After that we quantize the vector bundles with connection over the coadjoint orbits of the symmetry groupGL. Use the electric-magnetic duality to pass to the Langlands dual Lie groupG. Therefore, we have some affine Kac-Moody loop algebra of meromorphic functions with values in Lie algebra=Lie(G). Use the construction of Fock space reprsentations to have representations of such affine loop algebra. And finally, we have the automorphic representations of the corresponding Langlands-dual Lie groupsG.

scholarly journals Geometric Langlands correspondence for , over the pair of pants

2019 ◽  
Vol 155 (2) ◽  
pp. 324-371 ◽  
Author(s):  
David Nadler ◽  
Zhiwei Yun
Keyword(s):  
Projective Line ◽  
Langlands Correspondence ◽  
Geometric Langlands ◽  
Rank One ◽  
Tame Ramification

We establish the geometric Langlands correspondence for rank-one groups over the projective line with three points of tame ramification.

scholarly journals Preservation of depth in the local geometric Langlands correspondence

2016 ◽  
Vol 369 (2) ◽  
pp. 1345-1364 ◽  
Author(s):  
Tsao-Hsien Chen ◽  
Masoud Kamgarpour
Keyword(s):  
Langlands Correspondence ◽  
Geometric Langlands

Quantization of the Quantum Hitchin System and the Real Geometric Langlands Correspondence

2018 ◽  
pp. 347-384
Author(s):  
Jörg Teschner
Keyword(s):  
Generating Function ◽  
Quantization Condition ◽  
Local Systems ◽  
Langlands Correspondence ◽  
The Real ◽  
Hitchin System ◽  
Geometric Langlands ◽  
Langlands Programme

This chapter proposes a natural quantization condition for the Hitchin system and relate this to the generating function for the variety of opers within the Hitchin space of local systems. Links with the geometric Langlands programme are investigated.

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