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The α-Cosine Transform and Intertwining Integrals on Real Grassmannians

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Geometric Aspects of Functional Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2050))

Abstract

In this paper we describe the range of the α-cosine transform between real Grassmannians in terms of the decomposition under the action of the special orthogonal group. As one of the steps in the proof we show that the image of certain intertwining operators between maximally degenerate principal series representations is irreducible.

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Acknowledgements

We express our gratitude to T. Braden for the explanations of the results of [7], and to B. Rubin for communication us Proposition 2.2 and important remarks on the first version of the paper. We are grateful to A. Beilinson, J. Bernstein, A. Braverman, and D. Vogan for very useful discussions. We thank A. Koldobsky for useful discussions and some references.

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Authors and Affiliations

  1. Sackler Faculty of Exact Sciences, Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Semyon Alesker

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  1. Semyon Alesker
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Correspondence to Semyon Alesker .

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Editors and Affiliations

  1. Tel-Aviv, 69978, Israel

    Bo'az Klartag

  2. Technion Machine Learning Center, Technion, Israel Institute of Technology, Technion City, Haifa, 32000, Israel

    Shahar Mendelson

  3. Fac. Exact Sciences, School of Mathematical Sciences, University of Tel Aviv, Tel Aviv, 69978, Israel

    Vitali D. Milman

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Alesker, S. (2012). The α-Cosine Transform and Intertwining Integrals on Real Grassmannians. In: Klartag, B., Mendelson, S., Milman, V. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29849-3_1

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