Affine Demazure Modules and T -fixed Point Subschemes in the Affine Grassmannian
نویسنده
چکیده
Let G be a simple algebraic group of type A or D defined over C and T be a maximal torus of G. For a dominant coweight λ of G, the T -fixed point subscheme (Gr λ G) T of the Schubert variety Gr λ G in the affine Grassmannian GrG is a finite scheme. We prove that there is a natural isomorphism between the dual of the level one affine Demazure module corresponding to λ and the ring of functions (twisted by certain line bundle on GrG) of (Gr λ G) T . We use this fact to give a geometric proof of the FrenkelKac-Segal isomorphism between basic representations of affine algebras of A,D,E type and lattice vertex algebras.
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