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Maximal Poisson Commutative subalgebras for truncated parabolic subalgebras of maximal index in sln

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Abstract

We show that several properties of the semisimple algebras carry over to a certain family of parabolic subalgebras of maximal index in sln. More precisely we prove an analogue of Kostant's slice theorem [B. Kostant, Amer. J. Math. 85 (1963), 327-404] for these algebras and construct a maximal Poisson commutative subalgebra in the symmetric algebra, following the theory presented in [A.S. Mishchenko and A.T. Fomenko, Math. USSR-Izv. 12 (1978), 371-389]. These results are quite remarkable since these algebras do not admit appropriate sl2-triples.

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  1. Department of Mathematics, Weizmann Institute, Rehovot, 76100, Israel

    A. Joseph & P. Lamprou

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  1. A. Joseph
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  2. P. Lamprou
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Correspondence to A. Joseph or P. Lamprou.

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Joseph, A., Lamprou, P. Maximal Poisson Commutative subalgebras for truncated parabolic subalgebras of maximal index in sln. Transformation Groups 12, 549–571 (2007). https://doi.org/10.1007/s00031-006-0054-z

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  • DOI: https://doi.org/10.1007/s00031-006-0054-z

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