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Convexity and Commuting Hamiltonians
Author(s) -
Atiyah M. F.
Publication year - 1982
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/14.1.1
Subject(s) - convexity , citation , mathematics , mathematical economics , algebra over a field , combinatorics , discrete mathematics , computer science , library science , pure mathematics , financial economics , economics
The converse was proved by A. Horn [5], so that all points in this convex hull occur as diagonals of some matrix A with the given eigenvalues. Kostant [7] generalized these results to any compact Lie group G in the following manner. We consider the adjoint action of G on its Lie algebra L(G). If T is a maximal torus of G and W its Weyl group, then it is well known that W-orbits in L(T) correspond to G-orbits in L(G). Now fix a G-invariant metric on L(G), so that we can define orthogonal projection. Then Kostant's result isf