## A simple construction of Stein’s complementary series representations

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- by Siddhartha Sahi
- Proc. Amer. Math. Soc.
**108**(1990), 257-266 - DOI: https://doi.org/10.1090/S0002-9939-1990-0984813-7
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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

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## Bibliographic Information

- © Copyright 1990 American Mathematical Society
- 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