Character of Irreducible Representations Restricted to Finite Order Elements -- An Asymptotic Formula

2024/12/02 by Shrawan Kumar, Kumar, Shrawan, Dipendra Prasad +1
Computer Science · Mathematics · Physics and Astronomy · #22E46 #22F30 #Algebraic Geometry (math.AG) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Group Theory (math.GR) #Matrix Theory and Algorithms #Numerical methods for differential equations #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2412.01742

openalex publication_date 2024/12/02 · openalex created_date 2024/12/06 · openalex updated_date 2026/07/28

Abstract

Let G be a connected reductive group over the complex numbers and let T⊂ G be a maximal torus. For any t∈ T of finite order and any irreducible representation V(λ) of G of highest weight λ, we determine the character ch(t, V(λ)) by using the Lefschetz Trace Formula due to Atiyah-Singer and explicitly determining the connected components and their normal bundles of the fixed point subvariety (G/P)^t⊂ G/P (for any parabolic subgroup P). This together with Wirtinger's theorem gives an asymptotic formula for ch(t, V(nλ)) when n goes to infinity.

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