Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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FOCK REPRESENTATIONS OF THE NEISENBERG GROUP $H_R^(G,H)$

  • Published : 1997.05.01
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Abstract

In this paper, we introduce the Fock representation $U^{F, M}$ of the Heisenberg group $H_R^(g, h)$ associated with a positive definite symmetric half-integral matrix $M$ of degree h and prove that $U^{F, M}$ is unitarily equivalent to the Schrodinger representation of index $M$.

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References

  1. Proc. of Symposia in Pure Mathematics v.9 Quantum Mechanical Commutation Relations and Theta Functions P. Cartier
  2. Theta functions J. Igusa
  3. Ann. of Math. v.55 Induced Representations of Locally Compact Groups I G. W. Mackey
  4. Toroidal Compactification of Siegel Spaces, Lecture Notes in Math. Y. Namikawa
  5. Nagoya Math. J. v.123 Harmonic Analysis on theQuotient Spaces of Heisenberg Groups J.­H. Yang
  6. J. Number Theory v.49 Harmonic Analysis on the Quotient Spaces of Heisenberg Groups, II J.-H. Yang
  7. Japanese J. of Mathematics v.22 A decomposition theorem on differential polynomials of theta functions of high level J.-H. Yang
  8. Kyungpook Math. J. v.35 On theta functions J.-H. Yang
  9. preprint, MPI9716 Lattice representations of Heisenberg groups J.-H. Yang
  10. Proc. of the Workshops in Pure Mathematics on Groups and Algebraic Structures, the Korean Academic Council v.5 Unitary representations of the Heisenberg group $_R^{(g,h)_R}$ J.-H. Yang
  11. Hermite differential operators J.-H. Yang