Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22E50, 22E45, 22E46

Retrieve articles in all journals with MSC: 22E50, 22E45, 22E46


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