Discrete series representations and temperedness for the special linear group in two dimensions are introduced. These representations are classified abstractly, and weak containment in the regular representation is related to almost square integrability of diagonal matrix coefficients. The Weil representation of the metaplectic group in two dimensions is presented.

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Discrete Series Representations and Temperedness for SL2(ℝ)

  • Manfred Einsiedler,
  • Thomas Ward

摘要

Discrete series representations and temperedness for the special linear group in two dimensions are introduced. These representations are classified abstractly, and weak containment in the regular representation is related to almost square integrability of diagonal matrix coefficients. The Weil representation of the metaplectic group in two dimensions is presented.