, Volume 2, Issue 4, pp 375-390

A family of affine Weyl group representations

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Abstract

In this paper we explicitly determine the virtual representations of the finite Weyl subgroups of the affine Weyl group on the cohomology of the space of affine flags containing a family of elementsn t in an affine Lie algebra. We also compute the Euler characteristic of the space of partial flags containingn t and give a connection with hyperplane arrangements.

This paper forms part of my Ph.D. thesis at M.I.T. I was supported by an NSF Graduate Fellowship and NSF grant DMS 9304580.