The elliptic Weyl character formula

2012/06/04 by Nora Ganter · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Character (mathematics) #Geometry #Mathematics #Pure mathematics #math.AT #math.KT #math.RT #msc:19L47 #msc:22E67 #msc:55N34 #msc:55N91

paper · pdf · doi:10.1112/s0010437x1300777x

published as Compositio Math. 150 (2014) 1196-1234 · 44 pages

arxiv created 2012/06/04 · openalex publication_date 2014/05/12 · arxiv updated 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract We calculate equivariant elliptic cohomology of the partial flag variety \def \xmlpi #1\def \mathsfbi #1\boldsymbol \mathsf #1\let ≤ =\leqslant \let ≤ =\leqslant \let ≥ =\geqslant \let ≥ =\geqslant \def Pr \mathit Pr\def \Fr \mathit Fr\def \Rey \mathit ReG/H , where H⊆ G are compact connected Lie groups of equal rank. We identify the \rm RO(G) -graded coefficients E ll_G^* as powers of Looijenga’s line bundle and prove that transfer along the map \beginequation* π : G/H\longrightarrow \rm pt \endequation* is calculated by the Weyl–Kac character formula. Treating ordinary cohomology, K -theory and elliptic cohomology in parallel, this paper organizes the theoretical framework for the elliptic Schubert calculus of [N. Ganter and A. Ram, Elliptic Schubert calculus , in preparation].

Citations

• Equivariant K-theory and completion
• Elliptic Algebras and Equivariant Elliptic Cohomology
• A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications
• Equivariant cohomology, Koszul duality, and the localization theorem
• Géométrie algébrique et géométrie analytique
• The moment map and equivariant cohomology
• The Index of Elliptic Operators: I
• Central extensions of current groups in two dimensions

Cited by

• Hall algebra multiplication for stable envelopes on bow varieties
• Elliptic classes of Schubert varieties via Bott–Samelson resolution