A notion of rank for unitary representations of general linear groups

Author:
Roberto Scaramuzzi

Journal:
Trans. Amer. Math. Soc. **319** (1990), 349-379

MSC:
Primary 22E50; Secondary 22E46

MathSciNet review:
958900

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Abstract: A notion of rank for unitary representations of general linear groups over a locally compact, nondiscrete field is defined. Rank measures how singular a representation is, when restricted to the unipotent radical of a maximal parabolic subgroup. Irreducible representations of small rank are classified. It is shown how rank determines to a large extent the asymptotic behavior of matrix coefficients of the representations.

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DOI:
https://doi.org/10.1090/S0002-9947-1990-0958900-8

Article copyright:
© Copyright 1990
American Mathematical Society