|
Trudy Moskovskogo Matematicheskogo Obshchestva, 2018, Volume 79, Issue 1, Pages 1–95
(Mi mmo608)
|
|
|
|
This article is cited in 44 scientific papers (total in 44 papers)
Quantum $q$-Langlands correspondence
M. Aganagicab, E. Frenkela, A. Okounkovcde a Department of Mathematics,
University of California, Berkeley, USA
b Center for Theoretical Physics,
University of California, Berkeley, USA
c IITP, Moscow, Russia
d Department of Mathematics,
Columbia University, New York, USA
e Laboratory of Representation Theory
and Mathematical Physics,
Higher School of Economics, Moscow, Russia
Abstract:
We conjecture, and prove for all simply-laced Lie algebras, an identification
between the spaces of $q$-deformed conformal blocks for the deformed $\mathcal{
W}$-algebra $\mathcal{ W}_{q,t}(\mathfrak{g})$ and quantum affine algebra of
$\widehat{^L\mathfrak{g}}$, where $^L\mathfrak{g}$ is the Langlands dual Lie algebra to $\mathfrak{g}$.
We argue that this identification may be viewed as a manifestation of
a $q$-deformation of the quantum Langlands correspondence. Our proof relies on
expressing the $q$-deformed conformal blocks for both algebras in terms of the
quantum $\mathrm{K}$-theory of the Nakajima quiver varieties. The physical origin of the
isomorphism between them lies in the $\mathrm{6d}$ little string theory. The quantum
Langlands correspondence emerges in the limit in which the $\mathrm{6d}$ little string
theory becomes the $\mathrm{6d}$ conformal field theory with $(2,0)$ supersymmetry.
References: 130 entries.
Key words and phrases:
Landlands correspondence, $q$-conformal blocks.
Received: 15.04.2017 Revised: 20.05.2018
Citation:
M. Aganagic, E. Frenkel, A. Okounkov, “Quantum $q$-Langlands correspondence”, Tr. Mosk. Mat. Obs., 79, no. 1, MCCME, M., 2018, 1–95; Trans. Moscow Math. Soc., 2018, 1–83
Linking options:
https://www.mathnet.ru/eng/mmo608 https://www.mathnet.ru/eng/mmo/v79/i1/p1
|
Statistics & downloads: |
Abstract page: | 324 | Full-text PDF : | 146 | References: | 41 | First page: | 20 |
|