Abstract
Analysis on flag manifolds G ∕ P has connections to both representation theory and geometry; in this paper we show how one may derive some new Sobolev inequalities on spheres by combining rearrangement inequalities with analysis of principal series representations of rank-one semisimple Lie groups. In particular the Sobolev inequalities obtained involve hypoelliptic differential operators as opposed to elliptic ones in the usual case. One may hope that these ideas might in some form be extended to other parabolic geometries as well.
To Joseph A. Wolf, with admiration
Mathematics Subject Classification 2010: 22E45, 43A85
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Ørsted, B. (2013). Analysis on Flag Manifolds and Sobolev Inequalities. In: Huckleberry, A., Penkov, I., Zuckerman, G. (eds) Lie Groups: Structure, Actions, and Representations. Progress in Mathematics, vol 306. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7193-6_12
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DOI: https://doi.org/10.1007/978-1-4614-7193-6_12
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