Affine Hecke algebras associated to Kac-Moody groups

1995/08/24 by Howard Garland, Garland, H., I. Grojnowski +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9508019

openalex publication_date 1995/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a geometric construction of Cherednik's double affine Hecke algebra. We construct the algebra as the equivariant K-theory of the Lagrangian subvariety of the cotangent variety of the square of the flag variety of G, the variety being given by the union of the conormal bundles to the G-orbits on \flag×\flag. This is a generalisation of work of Kazhdan and Lusztig to the Kac-Moody case, and is suitable for describing a certain class of modules for this algebra. In a paper in preparation we will do this, in the case G is affine (Cherednik's case).

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• Completed Iwahori-Hecke algebra for Kac-Moody groups over local fields

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