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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Ultra-irreducibility of induced representations of semidirect products
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by Henrik Stetkær PDF
Trans. Amer. Math. Soc. 324 (1991), 543-554 Request permission

Abstract:

Let the Lie group $G$ be a semidirect product, $G = SK$, of a connected, closed, normal subgroup $S$ and a closed subgroup $K$. Let $\Lambda$ be a nonunitary character of $S$, and let ${K_\Lambda }$ be its stability subgroup in $K$. Let ${I^{\Lambda \mu }}$, for any irreducible representation $\mu$ of ${K_\Lambda }$, denote the representation ${I^{\Lambda \mu }}$ of $G$ induced by the representation $\Lambda \mu$ of $S{K_\Lambda }$. The representation spaces are subspaces of the distributions. We show that ${I^{\Lambda \mu }}$ is ultra-irreducible when the corresponding Poisson transform is injective, and find a sufficient condition for this injectivity.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 324 (1991), 543-554
  • MSC: Primary 22E45; Secondary 22D30
  • DOI: https://doi.org/10.1090/S0002-9947-1991-0974525-3
  • MathSciNet review: 974525