Open AccessThe structure of Hilbert flag varieties
Author(s) -
G.F. Helminck,
Aloysius G. Helminck
Publication year - 1994
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195165905
Subject(s) - flag (linear algebra) , mathematics , pure mathematics , general linear group , integrable system , context (archaeology) , realization (probability) , group (periodic table) , action (physics) , line (geometry) , algebra over a field , geometry , symmetric group , quantum mechanics , paleontology , statistics , physics , biology
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