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A simple construction of Stein's complementary series representations


Author: Siddhartha Sahi
Journal: Proc. Amer. Math. Soc. 108 (1990), 257-266
MSC: Primary 22E50; Secondary 22E45, 22E46
MathSciNet review: 984813
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Abstract: We given an elementary construction of Stein's complementary series for $ {\text{GL}}\left( {2n} \right)$ over an arbitrary local field $ \mathbb{F}$, and determine their restrictions to the "mirabolic" subgroup $ {P_{2n}} \approx {\text{GL}}\left( {2n - 1,\mathbb{F}} \right) \ltimes {\mathbb{F}^{2n - 1}}$. Taken together with the results in [S], this allows one to calculate the adduced representation $ A\pi $ for an arbitrary irreducible, unitary representation $ \pi $ of $ GL(n,\mathbb{C})$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-0984813-7
Keywords: Stein's complementary series, adduced representation
Article copyright: © Copyright 1990 American Mathematical Society