Analysis of the Brylinski-Kostant Model for Spherical Minimal Representations
2012 ◽
Vol 64
(4)
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pp. 721-754
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Keyword(s):
Abstract We revisit with another view point the construction by R. Brylinski and B. Kostant of minimal representations of simple Lie groups. We start froma pair (V,Q), where V is a complex vector space and Q a homogeneous polynomial of degree 4 on V. The manifold is an orbit of a covering of Conf(V,Q), the conformal group of the pair (V,Q), in a finite dimensional representation space. By a generalized Kantor-Koecher-Tits construction we obtain a complex simple Lie algebra 𝔤, and furthermore a real form 𝔤ℝ. The connected and simply connected Lie group Gℝ with Lie(Gℝ) = 𝔤ℝ acts unitarily on a Hilbert space of holomorphic functions defined on the manifold .
1966 ◽
Vol 27
(2)
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pp. 531-542
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2002 ◽
Vol 15
(5)
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pp. 527-532
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2014 ◽
Vol 150
(9)
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pp. 1579-1606
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2001 ◽
Vol 16
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pp. 4769-4801
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1993 ◽
Vol 08
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pp. 3479-3493
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1982 ◽
Vol 5
(2)
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pp. 315-335
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