2005/05/31 by Hjalmar Rosengren, Michael Schlosser · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Affine geometry #Affine plane (incidence geometry) #Affine representation #Affine transformation #Algebraic structures and combinatorial models #Macdonald polynomials #Mathematical proof #Polynomial #Root (linguistics) #math.CA #math.CO #msc:15A15 #msc:17B67 #msc:33E05
paper · pdf · doi:10.1112/s0010437x0600203x
published as Compositio Math. 142 (2006), 937-961 · 26 pages; minor modifications; to appear in Compositio Math
arxiv created 2005/10/21 · openalex publication_date 2006/07/01 · openalex created_date 2016/06/24 · arxiv updated 2019/02/22 · openalex updated_date 2026/08/05
We obtain several determinant evaluations, related to affine root systems, which provide elliptic extensions of Weyl denominator formulas. Some of these are new, also in the polynomial special case, while others yield new proofs of the Macdonald identities for the seven infinite families of irreducible reduced affine root systems.