Borel-Weil-Bott theory for Loop Groups

1997/07/17 by Constantin Teleman, Teleman, Constantin
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #alg-geom #hep-th #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9707014

4 pages, Mac-created PostScript. May display incorrectly but should print OK

arxiv created 1997/07/17 · openalex publication_date 1997/07/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note outlines the Borel-Weil-Bott theory for (arbitrary-genus) flag varieties of loop groups, following ideas of G. Segal. Recent revivalist interest in the "WZW fusion rules" suggests that my original (CMP 1995) treatment of the matter is not all that well understood, so a brief account thereof has been recycled along with the more recent results. Proofs are only outlined, with full details given in the references.

Related

• On the Siegel-Weil Theorem for Loop Groups (II)
• Equivariant correspondences and the Borel-Bott-Weil theorem
• Non-associative Loops for Holger Bech Nielsen
• Symmetries of KdV and Loop Groups
• Loops on schemes and the algebraic fundamental group