Instantons and Kähler geometry of nilpotent orbits View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1998

AUTHORS

Ranee Brylinski

ABSTRACT

The first obstacle in building a Geometric Quantization theory for nilpotent orbits of a real semisimple Lie group has been the lack of an invariant polarization. In order to generalize the Fock space construction of the quantum mechanical oscillator, a polarization of the symplectic orbit invariant under the maximal compact subgroup is required. In this paper, we explain how such a polarization on the orbit arises naturally from the work of Kronheimer and Vergne. This occurs in the context of hyperkähler geometry. The polarization is complex and in fact makes the orbit into a (positive) Kähler manifold. We study the geometry of this Kähler structure, the Vergne diffeomorphism, and the Hamiltonian functions giving the symmetry. We indicate how all this fits into a quantization program. More... »

PAGES

85-125

Book

TITLE

Representation Theories and Algebraic Geometry

ISBN

978-90-481-5075-5
978-94-015-9131-7

Author Affiliations

From Grant

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-015-9131-7_3

DOI

http://dx.doi.org/10.1007/978-94-015-9131-7_3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009453321


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