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

Harmonic analysis:

Fourier transform

Explicit Plancherel formula, Asai Rankin-Selberg integrals

Explicit Plancherel formula for the space of symplectic forms

Representation theory and arithmetic:

Howe duality

The symplectic representation

Calculations and interesting point of views:

Koszul duality, Categorical Plancherel formula

Equivariant cohomology

Moment maps and geometric invariant theory

Wave front sets

An Euler system of Heegner type

Schwartz space of basic affine space

Classics:

Luna’s theory of spherical systems, Primitive wonderful varieties

Spherical functions on a group of a p-adic type

Adams’ conjectures

Weyl integration formula, Plancherel formula for SL2

Factorization of Period Integrals

Arthur packets and Ramanujan conjecture, Satake isomorphism