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2 results

  • Quantization of the 4-Dimensional Nilpotent Orbit of Sl(3, ℝ)

  • Ranee Brylinski
  • Journal:
    Canadian Journal of Mathematics / Volume 49 / Issue 5 / 01 October 1997
    Published online by Cambridge University Press:
    20 November 2018, pp. 916-943
    Print publication:
    01 October 1997
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  • We give a new geometric model for the quantization of the 4-dimensional conical (nilpotent) adjoint orbit Oℝ of SL(3, ℝ). The space of quantization is the space of holomorphic functions on 𝕔 2 - {0}) which are square integrable with respect to a signed measure defined by a Meijer G-function. We construct the quantization out a non-flat Kaehler structure on 𝕔 2 - {0}) (the universal cover of Oℝ) with Kaehler potential ρ |z|4.

  • On the Equivariant Formality of Kähler Manifolds With Finite Group Action

  • Benjamin L. Fine, Georgia Triantafillou
  • Journal:
    Canadian Journal of Mathematics / Volume 45 / Issue 6 / 01 December 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 1200-1210
    Print publication:
    01 December 1993
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  • An appropriate definition of equivariant formality for spaces equipped with the action of a finite group G, and for equivariant maps between such spaces, is given. Kahler manifolds with holomorphic G-actions, and equivariant holomorphic maps between such Kàhler manifolds, are proven to be equivariantly formal, generalizing results of Deligne, Griffiths, Morgan, and Sullivan