Lusztig's conjecture for finite classical groups with even characteristic

2007/12/14 by Toshiaki Shoji, Shoji, Toshiaki
Mathematics · #20G05 #20G40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20G05 #msc:20G40

paper · pdf · doi:10.48550/arxiv.0712.2296

30 pages

arxiv created 2007/12/14 · openalex publication_date 2007/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The determination of scalars involved in Lusztig's conjecture for finite reductive groups G(F_q) was achieved by Waldspurger in the case of symplectic groups or orthogonal groups, under the condition that p,q are large enough. Here p is the characteristic of the finite field F_q. In this paper, we determine the scalars in the case of symplectic groups with p = 2, by applying the theory of symmetric spaces over a finite field due to Kawanaka and Lusztig. We also obtain a partial result in the case of special orthogonal groups with p = 2.

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