Hecke operators on de Rham cohomology
نویسندگان
چکیده
We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms.
منابع مشابه
Hecke Operators on Cohomology
Hecke operators play an important role in the theory of automorphic forms, and automorphic forms are closely linked to various cohomology groups. This paper is mostly a survey of Hecke operators acting on certain types of cohomology groups. The class of cohomology on which Hecke operators are introduced includes the group cohomology of discrete subgroups of a semisimple Lie group, the de Rham c...
متن کاملBRST Reduction of the chiral Hecke Algebra
We explore the relationship between de Rham and Lie algebra cohomologies in the finite dimensional and affine settings. In particular, given a ĝκmodule that arises as the global sections of a twisted D-module on the affine flag manifold, we show how to compute its BRST reduction modulo n(K) using the de Rham cohomology of the restrictions to N(K) orbits. A similar relationship holds between the...
متن کاملThe BRST reduction of the chiral Hecke algebra
We explore the relationship between de Rham and Lie algebra cohomologies in the finite dimensional and affine settings. In particular, given a ĝκ-module that arises as the global sections of a twisted D-module on the affine flag manifold, we show how to compute its untwisted BRST reduction modulo n(K) using the de Rham cohomology of the restrictions to N(K) orbits. A similar relationship holds ...
متن کاملDe Rham Theorem for Extended L 2 -cohomology
We prove an analogue of the de Rham theorem for the extended L 2-cohomology introduced by M.Farber [Fa]. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent in the sense of [GS] (i.e. with bounded morphisms and homotopy operators) to a combi...
متن کاملDe Rham Theorem for Extended L²-cohomology
We prove an analogue of the de Rham theorem for the extended L 2-cohomology introduced by M.Farber [Fa]. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent in the sense of [GS] (i.e. with bounded morphisms and homotopy operators) to a combi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014