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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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