For a
-adic field
, the space of
pro--Iwahori invariants of a
universal supersingular mod
representation
of
is
determined in the works of Breuil, Schein, and Hendel. The representation
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
of
,
making use of the Iwahori–Hecke operators. When
is not totally
ramified over
, the
representation
is a
nontrivial quotient of
.
We determine a basis for the space of invariants of
under the
pro--Iwahori
subgroup. A pleasant feature of this “new” representation
is that its space
of pro--Iwahori
invariants admits a more uniform description vis-à-vis the description of the space of
pro--Iwahori
invariants of
.
Keywords
modular representations, supersingular representations,
Iwahori–Hecke model