2023/12/08 by Gérard Laumon, Laumon, Gérard, Emmanuel Letellier +1
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Character (mathematics) #Computer science #FOS: Mathematics #Geometry #Geometry and complex manifolds #Group (periodic table) #Mathematical analysis #Mathematics #Orthogonality #Physics #Pure mathematics #Quantum mechanics #Relation (database) #Representation Theory (math.RT) #Table (database)
paper · pdf · doi:10.48550/arxiv.2312.05082
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Green functions were first introduced by Green to compute the character table of GLn(q) in 1955. They were later generalized by Deligne and Lusztig for an arbitrary finite group of Lie type G(q) using l-adic cohomological methods (1976). They proved that these Green functions satisfy an orthogonality relation (we call the first orthogonality relation). Ten years later Kawanaka proved that they satisfy an other orthogonality relation (we call the second orthogonality relation). In this notes, we provide a geometrical understanding of these two orthogonality relations and explain how we can see geometrically that the two orthogonality relations are in fact equivalent.