Iwahori-Hecke model for supersingular representations of GL2(Qp)

In this paper, we realize a regular supersingular representation π of GL2(Qp) as a quotient of a representation induced from the Iwahori subgroup of GL2(Qp). We also show that this realization provides a uniform way of looking at all the self-extensions of π which have a four dimensional space of I(1)-invariants.