English

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 GLGL-invariant measure on a semi-infinite Grassmannian over a finite field, describe the natural group of symmetries of this measure, and decompose the space L2L^2 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