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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
DOI: https://doi.org/10.1090/S0002-9939-1990-0984813-7
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 $GL(n,\mathbb {C})$.


References [Enhancements On Off] (What's this?)

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Keywords: Stein’s complementary series, adduced representation
Article copyright: © Copyright 1990 American Mathematical Society