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Gelfand Pairs Associated with Finite Heisenberg Groups

  • Chal Benson
  • Gail Ratcliff
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We examine a family of finite Gelfand pairs which arise in connection with Heisenberg groups H = H n (F) over finite fields of odd characteristic. The symplectic group Sp(n, F) acts on H by automorphisms. A subgroup K of Sp(n, F) yields a Gelfand pair (K, H) when the K-invariant functions on H commute under convolution. This is equivalent to the restriction of the oscillator representation to K being multiplicity free. An interesting example of this type occurs with K a finite analog of the unitary group U(n).

Keywords

Unitary Group Heisenberg Group Symplectic Group Borel Subgroup Oscillator Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Chal Benson
    • 1
  • Gail Ratcliff
    • 1
  1. 1.Department of MathematicsEast Carolina UniversityGreenville

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