Homological dimension of simple pro-p-Iwahori--Hecke modules

2015/12/01 by Koziol, Karol
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1512.00247

Abstract

Let G be a split connected reductive group defined over a nonarchimedean local field of residual characteristic p, and let H be the pro-p-Iwahori--Hecke algebra associated to a fixed choice of pro-p-Iwahori subgroup. We explore projective resolutions of simple right H-modules. In particular, subject to a mild condition on p, we give a classification of simple right H-modules of finite projective dimension, and consequently show that "most" simple modules have infinite projective dimension.

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