nLab
Hecke correspondence

Contents

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.

Properties

Relation to S-duality in super Yang-Mills theory

geometric Langlands correspondenceS-duality in N=4 D=4 super Yang-Mills theory
Hecke transformation't Hooft operator
local system/flat connectionelectric eigenbrane (eigenbrane of Wilson operator)
Hecke eigensheafmagnetic eigenbrane (eigenbrane of 't Hooft operator )

(Kapustin-Witten 06)

References

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