The structure of Hilbert flag varieties


Helminck, Gerard F. and Helminck, Aloysius G. (1994) The structure of Hilbert flag varieties. Publications of the Research Institute for Mathematical Sciences, 30 (3). pp. 401-441. ISSN 0034-5318

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Abstract:In this paper we present a geometric realization of infinite dimensional analogues of the finite dimensional representations of the general linear group. This requires and etailed analysis of the structure of the flag varieties involved and the line bundles over them. In general the action of the restricted linear group can not be lifted to the line bundles and thus leads to central extensions of this group. It is determined exactly when these extensions are non-trivial. These representations are of importance in quantum field theory and in the framework of integrable systems. As an application, it is shown how the flag varieties occur in the latter context.
Item Type:Article
Additional information:Open access
Copyright:© 1994 Institute of Mathematical Statistics
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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