Parabolic induction in the homotopy category of pro-p Iwahori-Hecke modules

2023/12/19 by Dupré, Nicolas
#18N40 #18N55 #20C08 #Category Theory (math.CT) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2312.12238

Abstract

Let G be the group of rational points of a split connected reductive group over a non-archimedean local field of residue characteristic p, and let H denote the pro-p Iwahori-Hecke algebra of G over a field of characteristic p. We study the parabolic induction functor for H-modules in terms of the Gorenstein projective model structures introduced by Hovey. Let Ho(H) denote the associated homotopy category of this model structure. We show that Ho(H) and its thick subcategory generated by the essential images of finitely many parabolic induction functors are related via a recollement of triangulated categories. We then investigate the isomorphism classes of simple H-modules in Ho(H) and give a complete classification for simple supersingulars when G=GL_n.

Related

• Parabolic induction in characteristic p
• Model categories and pro-p Iwahori-Hecke modules
• Derived parabolic induction
• Pro-p Iwahori-Hecke algebras are Gorenstein
• Modulo p parabolic induction of pro-p-Iwahori Hecke algebra