2017/01/12 by Zongbin Chen, Chen, Zongbin
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1701.03202
openalex publication_date 2017/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explain an algorithm to calculate Arthur's weighted orbital integral in terms of the number of rational points on the fundamental domain of the associated affine Springer fiber. The strategy is to count the number of rational points of the truncated affine Springer fibers in two ways: by the Arthur-Kottwitz reduction and by the Harder-Narasimhan reduction. A comparison of results obtained from these two approaches gives us recurrence relations between the number of rational points on the fundamental domains of the affine Springer fibers and Arthur's weighted orbital integrals. As an example, we calculate Arthur's weighted orbital integrals for the group GL2 and GL3.