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arXiv:1209.3477 [math.RT]AbstractReferencesReviewsResources

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

Yury A. Neretin

Published 2012-09-16, updated 2013-09-28Version 2

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.

Comments: 32pp
Journal: Advances in Mathematics Volume 250, 15, 2014, Pages 320-350
Categories: math.RT, math.CA, math.PR
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