The Eichler cohomology groups and automorphic forms

Some New Results on the Eichler Cohomology of Automorphic Forms

We here formulate and prove several new results concerning the Eichler cohomology of automorphic forms on finitely generated Fuchsian groups of the first kind and, in particular, on //-groups. The Eichler cohomology we introduce is connected with automorphic forms of arbitrary real degree (as opposed to integral degree), with a suitably chosen underlying space of functions analytic in the upper...

Cohomology of Arithmetic Groups and Periods of Automorphic Forms

(1) Firstly, I gave a brief introduction to the cohomology of arithmetic groups, in particular the fact that the “tempered” (informally: “near the middle dimension”’) part of the cohomology looks like the cohomology of a torus. This corresponds to §2, §3, §4 of these notes. For the reader totally unfamiliar with the cohomology of arithmetic groups, §3 might be the best thing to focus on. (2) Ne...

Discontinuous Groups and Automorphic Forms

Automorphic Forms and Metaplectic Groups

In 1952, Gelfand and Fomin noticed that classical modular forms were related to representations of SL2(R). As a result of this realization, Gelfand later defined GLr automorphic forms via representation theory. A metaplectic form is just an automorphic form defined on a cover of GLr, called a metaplectic group. In this talk, we will carefully construct the metaplectic covers of GL2(F) where F i...

Hodge Domains and Automorphic Cohomology

I. Background material 1 A. Mumford-Tate groups and domains B. The structure theorem for global variations of Hodge structure C. Hodge groups and domains II. General context A. Algebro-geometric B. Representation theoretic C. Arithmetic III. Cyclic spaces and their enlargements A. General definitions and some properties B. Two examples C. Enlargements of cycle spaces IV. Penrose-Radon transform...