2023/06/30 by Teppei Takamatsu, Takamatsu, Teppei
Mathematics · #11G25 #20G25 #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2306.17382
openalex publication_date 2023/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that Lusztig's semi-infinite Deligne--Lusztig variety for GSp (and its inner form) is isomorphic, as a set with action, to an affine Deligne--Lusztig variety at infinite level, generalizing a result of Chan--Ivanov. Furthermore, we show that a component of some affine Deligne--Lusztig variety X0wr(b)L for GSp can be written, up to perfection, as a direct product of a classical Deligne--Lusztig variety with an affine space. We also study the varieties Xh defined by Chan and Ivanov, and show that Xh at infinite level can be realized as a subset of semi-infinite Deligne--Lusztig varieties defined using components of affine Deligne--Lusztig varieties such as X0wr(b)L above, even in the GSp case. This reinterprets previous constructions of representations from Xh as instances of Lusztig's conjectural picture.