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Equations for a filtration of sheets and the variety of singular elements of a complex semisimple Lie algebra

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Representations of Reductive Groups

Part of the book series: Progress in Mathematics ((PM,volume 312))

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Abstract

This paper connects results on Amitsur–Levitski identities for simple Lie algebras, ideals in Borel subalgebras, commutative Lie subalgebras in simple Lie algebras, filtration of sheets, and recent work with Nolan Wallach on the variety of singular elements in a complex semisimple Lie algebra.

To David Vogan whose brilliant mathematical career continues to exhibit an ever-increasing number of contributions to mathematics

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References

  1. Bertram Kostant, A Theorem of Frobenius, A Theorem of Amitsur-Levitski and Cohomology Theory, J. Math. and Mech., 7 (1958): 2, Indiana University, 237–264.

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  4. Bertram Kostant, A Lie Algebra Generalization of the Amitsur-Levitski Theorem, Adv. In Math. 40 (1981):2, 155–175.

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  5. Bertram Kostant and N. Wallach, On the algebraic set of singular elements in a complex simple Lie algebra, in: Representation Theory and Mathematical Physics, Conf. in honor of Gregg Zuckerman’s 60th Birthday, Contemp. Math., 557, Amer. Math. Soc., 2009, pp. 215–230.

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Acknowledgements

I want to thank the referee for his thoughtful and helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, M.I.T., Cambridge, MA, 02139, USA

    Bertram Kostant

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  1. Bertram Kostant
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Correspondence to Bertram Kostant .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada

    Monica Nevins

  2. Dept of Mathematics and Statistics, University of Utah, Salt Lake City, Utah, USA

    Peter E. Trapa

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Kostant, B. (2015). Equations for a filtration of sheets and the variety of singular elements of a complex semisimple Lie algebra. In: Nevins, M., Trapa, P. (eds) Representations of Reductive Groups. Progress in Mathematics, vol 312. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-23443-4_11

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