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On the Segal-Shale-Weil representations and harmonic polynomials. (English) Zbl 0375.22009

22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
22E30 Analysis on real and complex Lie groups
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
43A32 Other transforms and operators of Fourier type
43A85 Harmonic analysis on homogeneous spaces
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