We study a compact invariant convex set E in a polar representation of a compact Lie group. Polar rapresentations are given by the adjoint action of K on p, where K is a maximal compact subgroup of a real semisimple Lie group G with Lie algebra g=k⊕p. If a⊂p is a maximal abelian subalgebra, then P=E∩a is a convex set in a. We prove that up to conjugacy the face structure of E is completely determined by that of P and that a face of E is exposed if and only if the corresponding face of P is exposed. We apply these results to the convex hull of the image of a restricted momentum map.

invariant convex sets in polar representations / Biliotti, Leonardo; Ghigi, A.; Heinzner, P.. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 213:june 2016, 1(2016), pp. 1-423. [10.1007/s11856-016-1325-6]

invariant convex sets in polar representations

BILIOTTI, Leonardo;
2016-01-01

Abstract

We study a compact invariant convex set E in a polar representation of a compact Lie group. Polar rapresentations are given by the adjoint action of K on p, where K is a maximal compact subgroup of a real semisimple Lie group G with Lie algebra g=k⊕p. If a⊂p is a maximal abelian subalgebra, then P=E∩a is a convex set in a. We prove that up to conjugacy the face structure of E is completely determined by that of P and that a face of E is exposed if and only if the corresponding face of P is exposed. We apply these results to the convex hull of the image of a restricted momentum map.
2016
invariant convex sets in polar representations / Biliotti, Leonardo; Ghigi, A.; Heinzner, P.. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 213:june 2016, 1(2016), pp. 1-423. [10.1007/s11856-016-1325-6]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2778529
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