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All algebras of spherical functions defined on the two-by-two general linear group with entries in a locally compact $ p$-adic field are commutative.


Author: Allan J. Silberger
Journal: Proc. Amer. Math. Soc. 21 (1969), 437-440
MSC: Primary 22.20
DOI: https://doi.org/10.1090/S0002-9939-1969-0237707-8
MathSciNet review: 0237707
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References [Enhancements On Off] (What's this?)

  • [1] A. A. Kirillov, Infinite-dimensional unitary representations of a second-order matrix group with elements in a locally compact field, Dokl. Akad. Nauk SSSR 150 (1963), 740-743 = Soviet Math. Dokl. 4 (1963), 748-752. MR 0151552 (27:1537)
  • [2] F. I. Mautner, Spherical functions over p-adic fields. II, Amer. J. Math. 86 (1964), 171-200. MR 0166305 (29:3582)

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DOI: https://doi.org/10.1090/S0002-9939-1969-0237707-8
Article copyright: © Copyright 1969 American Mathematical Society

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