Invariant integral on classical groups and algebraic harmonic analysis

Alvarez, Amelia; Sancho, Carlos; Sancho, Pedro

Invariant integral on classical groups and algebraic harmonic analysis

Authors

Alvarez, Amelia

Sancho, Carlos

Sancho, Pedro

Description

Let $G={\rm Spec} A$ be a linearly reductive group and let $w_G\in A^*$ be the invariant integral on $G$. We establish the harmonic analysis on $G$ and we compute $w_G$ when $G=Sl_n, Gl_n, O_n, Sp_{2n}$ by geometric arguments and by means of the Fourier transform.
17 pages, some new results added