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Constructions of SU(2) and Weyl equivari...
Malkoun, Joseph...

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Constructions of SU(2) and Weyl equivariant maps for all classical groups by Malkoun, Joseph ( Author )
Lemonjar Open Access
N.A
17-08-2015
If G is a compact Lie group, T a maximal torus in G (with Lie algebras g and t respectively) and W the corresponding Weyl group, then the Berry-Robbins problem for G, as formulated by Sir Michael Atiyah and Roger Bielawski, asks whether there exists a continuous SU(2)×W equivariant map from the space of regular Cartan triples (an open subset of t⊗R3) to G/T, where SU(2) acts via a regular Lie group homomorphism SU(2)→G. This was settled positively by Atiyah and Bielawski, and their maps are even smooth, but they are not explicit. For G=U(n), there exists another construction due to Sir Michael Atiyah and developed further with Paul Sutcliffe, which is explicit, but relies on a linear independence conjecture. The author had previously found a similar type of construction for G=Sp(m), also relying on a linear independence conjecture. In this paper, similar constructions are done for SO(2m+1) and SO(2m), thus exhausting the list of classical groups.
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http://arxiv.org/abs/1508.04076
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