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arXiv · 1209.3477

The space $L^2$ on semi-infinite Grassmannian over finite field

Yury A. Neretin
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Abstract

We construct a $GL$-invariant measure on a semi-infinite Grassmannian over a finite field, describe the natural group of symmetries of this measure, and decompose the space $L^2$ 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.

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BibTeXRIS

Yury A. Neretin. 2013-09-28. The space $L^2$ on semi-infinite Grassmannian over finite field. https://doi.org/10.1016/j.aim.2013.09.014

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