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NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT
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Geometry-Algebra-Singularities-Combinatorics Seminar
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Centralizers of Nilpotents and the Bala-Carter classification
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Alfred Noël U. Mass. Boston
Northeastern University 509 Lake Hall 1:30 p.m., Monday, June 7, 1999
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Abstract: The centralizer of a nilpotent element, in the adjoint Lie group of the Lie algebra containing it, may not be a connected group. This means that the quotient of the centralizer modulo its connected component containing the identity element is often a non-trivial (finite) group. Recently, Eric Sommers has given a unified approach for computing the conjugacy classes of this quotient for complex simple algebras using the Bala-Carter classification of complex nilpotent orbits. We intend to show that his approach can be extended to complex symmetric spaces and hence to reductive real Lie groups. Information about the centralizer of nilpotents is needed to construct irreducible unitary representations of such groups. This is joint work with Donald King at Northeastern University.
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Geometry-Algebra-Singularities-Combinatorics home page:
http://www.math.neu.edu/~suciu/GASC.html
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