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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Solvable groups and quadratic forms


Author: Richard Tolimieri
Journal: Trans. Amer. Math. Soc. 201 (1975), 329-345
MSC: Primary 10C05; Secondary 12A45, 22E45
DOI: https://doi.org/10.1090/S0002-9947-1975-0354552-0
MathSciNet review: 0354552
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Abstract: A solvable Lie group and a unitary representation are constructed from a given binary quadratic form. The multiplicity of this representation is related to the arithmetic of the form.


References [Enhancements On Off] (What's this?)

  • [1] L. Auslander and J. Brezin, Fibre bundle structures and harmonic analysis on Heisenberg manifolds, Proc. Maryland Conference on Harmonic Analysis, Springer-Verlag, New York, 1973.
  • [2] J. Brezin, Function theory on metabelian solvmanifolds, J. Functional Analysis 10 (1972), 33–51. MR 0348401
  • [3] George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 0044536, https://doi.org/10.2307/1969423
  • [4] C. L. Siegel, Lectures on quadratic forms, Notes by K. G. Ramanathan. Tata Institute of Fundamental Research Lectures on Mathematics, No. 7, Tata Institute of Fundamental Research, Bombay, 1967. MR 0271028

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0354552-0
Keywords: Solvable groups, unitary representation, quadratic form, multiplicity
Article copyright: © Copyright 1975 American Mathematical Society