An exotic Springer correspondence for symplectic groups

2006/07/19 by Syu Kato, Kato, Syu
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0607478

v2; 16pp. title changed, Nov/07 version except for one reference, may be merged into next revision of math.RT/0601155

openalex publication_date 2006/07/19 · arxiv created 2008/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a sequel to math.RT/0601155. Let G be a complex symplectic group. In math.RT/0601155, we constructed a certain G-variety N = N₁, which we call the (1-) exotic nilpotent cone. In this paper, we study the set of G-orbits of the variety N. It turns out that the variety N gives a variant of the Springer correspondence for the Weyl group of type C, but shares a similar flavor with that of type A case. (I.e. there appears no non-trivial local system and the correspondence is bijective.) As an application, we present one sufficient condition for the bijectivity of our exotic Deligne-Langlands correspondence [K1].

Related

• Exotic symmetric space over a finite field, I
• An exotic Springer correspondence for F₄
• An exotic nilpotent cone for symplectic group
• Springer theory for symplectic Galois groups
• Formality for the nilpotent cone and a derived Springer correspondence