scholarly journals Hofstadter’s butterfly and Langlands duality

2018 ◽  
Vol 59 (6) ◽  
pp. 061704 ◽  
Author(s):  
Kazuki Ikeda
Keyword(s):  
Langlands Duality

scholarly journals SEIBERG–WITTEN PREPOTENTIAL FROM WZNW CONFORMAL BLOCK: LANGLANDS DUALITY AND SELBERG TRACE FORMULA

2012 ◽  
Vol 27 (22) ◽  
pp. 1250129
Author(s):  
TA-SHENG TAI
Keyword(s):  
Trace Formula ◽  
Conformal Block ◽  
Selberg Trace Formula ◽  
Conformal Blocks ◽  
Langlands Duality

We show how SU(2) Nf = 4 Seiberg–Witten prepotentials are derived from [Formula: see text] four-point conformal blocks via considering Langlands duality.

scholarly journals Poincaré duality and Langlands duality for extended affine Weyl groups

2018 ◽  
Vol 3 (3) ◽  
pp. 491-522
Author(s):  
Graham Niblo ◽  
Roger Plymen ◽  
Nick Wright
Keyword(s):  
Weyl Groups ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Affine Weyl Groups ◽  
Langlands Duality

scholarly journals Stratified Langlands duality in the $A_n$ tower

2019 ◽  
Vol 13 (1) ◽  
pp. 193-225
Author(s):  
Graham Niblo ◽  
Roger Plymen ◽  
Nick Wright
Keyword(s):  
Langlands Duality

scholarly journals Geometric Langlands duality and the equations of Nahm and Bogomolny

2010 ◽  
Vol 140 (4) ◽  
pp. 857-895 ◽  
Author(s):  
Edward Witten
Keyword(s):  
Gauge Theory ◽  
Lie Group ◽  
Moduli Space ◽  
Dual Group ◽  
Langlands Duality ◽  
Geometric Langlands

Geometric Langlands duality relates a representation of a simple Lie group Gv to the cohomology of a certain moduli space associated with the dual group G. In this correspondence, a principal SL2 subgroup of Gv makes an unexpected appearance. This can be explained using gauge theory, as this paper will show, with the help of the equations of Nahm and Bogomolny.

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 Langlands duality for representations of quantum groups

2010 ◽  
Vol 349 (3) ◽  
pp. 705-746 ◽  
Author(s):  
Edward Frenkel ◽  
David Hernandez
Keyword(s):  
Quantum Groups ◽  
Langlands Duality

scholarly journals LANGLANDS DUALITY IN LIOUVILLE-$H^3_+$ WZNW CORRESPONDENCE

2009 ◽  
Vol 24 (16n17) ◽  
pp. 3137-3170 ◽  
Author(s):  
GASTON GIRIBET ◽  
YU NAKAYAMA ◽  
LORENA NICOLÁS
Keyword(s):  
Correlation Functions ◽  
Free Field ◽  
Liouville Theory ◽  
Hamiltonian Reduction ◽  
Langlands Correspondence ◽  
Conformal Field ◽  
Langlands Duality ◽  
Dual Version ◽  
Free Field Realization ◽  
Wznw Model

We show a physical realization of the Langlands duality in correlation functions of [Formula: see text] WZNW model. We derive a dual version of the Stoyanovky–Riabult–Teschner (SRT) formula that relates the correlation function of the [Formula: see text] WZNW and the dual Liouville theory to investigate the level duality k - 2 → (k - 2)-1 in the WZNW correlation functions. Then, we show that such a dual version of the [Formula: see text]-Liouville relation can be interpreted as a particular case of a biparametric family of nonrational conformal field theories (CFT's) based on the Liouville correlation functions, which was recently proposed by Ribault. We study symmetries of these new nonrational CFT's and compute correlation functions explicitly by using the free field realization to see how a generalized Langlands duality manifests itself in this framework. Finally, we suggest an interpretation of the SRT formula as realizing the Drinfeld–Sokolov Hamiltonian reduction. Again, the Hamiltonian reduction reveals the Langlands duality in the [Formula: see text] WZNW model. Our new identity for the correlation functions of [Formula: see text] WZNW model may yield a first step to understand quantum geometric Langlands correspondence yet to be formulated mathematically.

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