Langlands duality and global Springer theory
نویسندگان
چکیده
منابع مشابه
Gauge Theory and Langlands Duality
In the late 1960s Robert Langlands launched what has become known as the Langlands Program with the ambitious goal of relating deep questions in Number Theory to Harmonic Analysis [L]. In particular, Langlands conjectured that Galois representations and motives can be described in terms of the more tangible data of automorphic representations. A striking application of this general principle is...
متن کاملRepresentation theory, geometric Langlands duality and categorification
The representation theory of reductive groups, such as the group GLn of invertible complex matrices, is an important topic, with applications to number theory, algebraic geometry, mathematical physics, and quantum topology. One way to study this representation theory is through the geometric Satake correspondence (also known as geometric Langlands duality). This correspondence relates the geome...
متن کاملLocal Langlands Duality and a Duality of Conformal Field Theories
We show that the numerical local Langlands duality for GLn and the T-duality of twodimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local Fourier transform in both its `-adic and complex incarnation gives rise to symmetries of arithmetic and geometric local Langlands parameters.
متن کاملAffine Algebras, Langlands Duality and Bethe Ansatz
By Langlands duality one usually understands a correspondence between automorphic representations of a reductive group G over the ring of adels of a field F , and homomorphisms from the Galois group Gal(F/F ) to the Langlands dual group GL. It was originally introduced in the case when F is a number field or the field of rational functions on a curve over a finite field [1]. Recently A. Beilins...
متن کاملMirror Symmetry, Hitchin’s Equations, and Langlands Duality
Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold C. But understanding these statements is extremely difficult without picking a complex structure on C and using Hitchin’s equations. We sketch the essential statements both for the “unramified” case that C is a compact oriented two-mani...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2012
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x11007433