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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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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