Notes

I write some notes, which reflect my understanding and interests on automorphic representation theory and its related fields.

Algebraic groups and Lie groups:

Smooth affine spherical varieties

Structure theory of Whittaker induction

Integral representation of L-functions:

Examples:

Explicit formula for Shalika models

Unramified computation for strongly tempered spherical varieties

AI assisted examples:

Open periods for basic spherical varieties

Computation of the unramified Plancherel measure

LLC for covering groups, Dual groups for covering groups

Classics:

Luna’s theory of spherical systems, Primitive wonderful varieties

Factorization of Period Integrals

Arthur packets and Ramanujan conjecture

Endoscopic classification of representations, Base change for GL(2), Base change and the advanced theory of the trace formula