Generalized principal series representations of $SL(1+n,\mathbb {C})$
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Publication:4372343
DOI10.1090/S0002-9939-97-03877-XzbMath0883.22012OpenAlexW1505909715MaRDI QIDQ4372343
Genkai Zhang, Anthony H. Dooley
Publication date: 11 December 1997
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03877-x
Semisimple Lie groups and their representations (22E46) Harmonic analysis and spherical functions (43A90)
Related Items (3)
Structure of the degenerate principal series on symmetric \(R\)-spaces and small representations ⋮ The Cos\(^\lambda\) and Sin\(^\lambda\) transforms as intertwining operators between generalized principal series representations of SL\((n+1,\mathbb K)\) ⋮ Branching laws for small unitary representations of GL(n, ℂ)
Cites Work
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- Recurrence formulas for zonal polynomials
- Unitary representations of reductive Lie groups
- The unitary dual of \(\mathrm{GL}(n)\) over an archimedean field
- Harmonic analysis on the quantized Riemann sphere
- Degenerate principal series and compact groups
- Jordan algebras and Capelli identities
- The Plancherel formula for spherical functions with a one-dimensional \(K\)-type on a simply connected simple Lie group of Hermitian type
- Relative discrete series of line bundles over bounded symmetric domains
- Jordan algebras and generalized principal series representations
- Generalized principal series representations and tube domains
- Realization of Hermitian symmetric spaces as generalized half-planes
- Analysis in matrix spaces and some new representations of \(SL(N,\mathbb{C})\)
- One-dimensional $K$-types in finite dimensional representations of semisimple Lie groups: A generalization of Helgason's theorem.
- Elementary spherical functions on symmetric spaces.
- Weighted Plancherel formula. Irreducible unitary representations and eigenspace representations.
- A weighted Plancherel formula II. The case of the ball
- Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations
- Some Recurrence Formulas for Spherical Polynomials on Tube Domains
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