The Embeddings of the Discrete Series in the Principal Series for Semisimple Lie Groups of Real Rank One

1980 ◽  
Vol 261 (2) ◽  
pp. 303 ◽  
Author(s):  
M. Welleda ◽  
Baldoni Silva
Keyword(s):  
Lie Groups ◽  
Discrete Series ◽  
Principal Series ◽  
Real Rank ◽  
Semisimple Lie Groups ◽  
Rank One

Whittaker Functions on Real Semisimple Lie Groups of Rank Two

2010 ◽  
Vol 62 (3) ◽  
pp. 563-581 ◽  
Author(s):  
Taku Ishii
Keyword(s):  
Lie Groups ◽  
Principal Series ◽  
Real Rank ◽  
Whittaker Functions ◽  
Semisimple Lie Groups ◽  
Explicit Formulas ◽  
Series Representations ◽  
Principal Series Representations

AbstractWe give explicit formulas forWhittaker functions on real semisimple Lie groups of real rank two belonging to the class one principal series representations. By using these formulas we compute certain archimedean zeta integrals.

scholarly journals Invariant trilinear forms on spherical principal series of real rank one semisimple Lie groups

2014 ◽  
Vol 25 (03) ◽  
pp. 1450017 ◽  
Author(s):  
Salem Ben Said ◽  
Khalid Koufany ◽  
Genkai Zhang
Keyword(s):  
Hypergeometric Functions ◽  
Integral Formula ◽  
Principal Series ◽  
Intertwining Operators ◽  
Real Rank ◽  
Semisimple Lie Groups ◽  
Smooth Functions ◽  
Trilinear Form ◽  
Finite Center ◽  
Rank One

Let G be a connected semisimple real-rank one Lie group with finite center. We consider intertwining operators on tensor products of spherical principal series representations of G. This allows us to construct an invariant trilinear form [Formula: see text] indexed by a complex multiparameter [Formula: see text] and defined on the space of smooth functions on the product of three spheres in 𝔽n, where 𝔽 is either ℝ, ℂ, ℍ, or 𝕆 with n = 2. We then study the analytic continuation of the trilinear form with respect to (ν1, ν2, ν3), where we locate the hyperplanes containing the poles. Using a result due to Johnson and Wallach on the so-called "partial intertwining operator", we obtain an expression for the generalized Bernstein–Reznikov integral [Formula: see text] in terms of hypergeometric functions.

scholarly journals The fourier transform on semisimple lie groups of real rank one

1973 ◽  
Vol 131 (0) ◽  
pp. 1-26 ◽  
Author(s):  
Paul J. Sally ◽  
Garth Warner
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Real Rank ◽  
Semisimple Lie Groups ◽  
Rank One ◽  
The Fourier Transform

scholarly journals A geometric construction of the discrete series for semisimple Lie groups

1979 ◽  
Vol 54 (2) ◽  
pp. 189-192 ◽  
Author(s):  
Michael Atiyah ◽  
Wilfried Schmid
Keyword(s):  
Lie Groups ◽  
Discrete Series ◽  
Geometric Construction ◽  
Semisimple Lie Groups
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