nLab
Hecke correspondence

Idea

A Hecke correspondence is a certain correspondence between a moduli stacks of bundles. The integral transform induced by a Hecke correspondence is called a Hecke transform. The objects preserves by such a transform up to a tensor multiple are called Hecke eigensheaves

These are central objects of interest in geometric Langlands duality.

geometric Langlands correspondence	S-duality in N=4 D=4 super Yang-Mills theory
Hecke transformation	't Hooft operator
local system/flat connection	electric eigenbrane (eigenbrane of Wilson operator)
Hecke eigensheaf	magnetic eigenbrane (eigenbrane of 't Hooft operator )

Edward Frenkel, section 3.7 in Lectures on the Langlands Program and Conformal Field Theory (arXiv:hep-th/0512172)

Last revised on July 2, 2014 at 11:19:17. See the history of this page for a list of all contributions to it.