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Geometry of infinite dimensional Grassmannians and the Mickelsson-Rajeev cocycle | | Danny Stevenson
; | | Date: |
25 Feb 2008 | | Abstract: | In their study of the representation theory of loop groups, Pressley and
Segal introduced a determinant line bundle over an infinite dimensional
Grassmann manifold. Mickelsson and Rajeev subsequently generalized the work of
Pressley and Segal and in the process introduced for any p >=1 another infinite
dimensional Grassmann manifold and a determinant line bundle defined over it.
The construction of this determinant line bundle required the notion of a
regularized determinant for bounded operators. In this note we specialize to
the case p =2 and construct explicitly a connection on the corresponding
determinant line bundle and give a simple and explicit formula for its
curvature. As an application of our results we give a geometric derivation of
the Mickelsson-Rajeev cocycle. | | Source: | arXiv, 0802.3608 | | Services: | Forum | Review | PDF | Favorites | |
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