The space $L^2$ on semi-infinite Grassmannian over finite field
Representation Theory
2014-06-26 v2 Classical Analysis and ODEs
Probability
Abstract
We construct a -invariant measure on a semi-infinite Grassmannian over a finite field, describe the natural group of symmetries of this measure, and decompose the space over the Grassmannian on irreducible representations. The spectrum is discrete, spherical functions on the Grassmannian are given in terms of the Al Salam--Carlitz orthogonal polynomials. We also construct an invariant measure on the corresponding space of flags.
Keywords
Cite
@article{arxiv.1209.3477,
title = {The space $L^2$ on semi-infinite Grassmannian over finite field},
author = {Yury A. Neretin},
journal= {arXiv preprint arXiv:1209.3477},
year = {2014}
}
Comments
32pp