IWAHORI-HECKE MODEL FOR MOD p REPRESENTATIONS OF GL(2, F)

For a p-adic field F, the space of pro- p-Iwahori invariants of a universal supersingular mod p representation τ of GL2(F) is determined in the works of Breuil, Schein, and Hendel. The representation t is introduced by Barthel and Livné and is defined in terms of the spherical Hecke operator. In Anandavardhanan and Borisagar [2013; 2015], an Iwahori-Hecke approach was introduced to study these universal supersingular representations in which they can be characterized via the Iwahori-Hecke operators. In this paper, we construct a certain quotient π of τ, making use of the Iwahori-Hecke operators. When F is not totally ramified over (Formula presented), the representation π is a nontrivial quotient of τ. We determine a basis for the space of invariants of π under the pro-p-Iwahori subgroup. A pleasant feature of this “new” representation π is that its space of pro-p-Iwahori invariants admits a more uniform description vis-à-vis the description of the space of pro-p-Iwahori invariants of τ.