Freeness of spherical Hecke modules of unramified $U(2,1)$ in characteristic $p$

Abstract

Let $F$ be a non-archimedean local field of odd residue characteristic $p$. Let $G$ be the unramified unitary group $U(2,1)(E/F)$ in three variables, and $K$ be a maximal compact open subgroup of $G$. For an irreducible smooth representation $\sigma$ of $K$ over ${\overline{\mathbf{F}}}_p$, we prove that the compactly induced representation ${\text{ind}}_K^G\sigma$ is free of infinite rank over the spherical Hecke algebra $\mathcal{H}(K,\sigma )$.

Final version, to appear in Journal of Number Theory

References in corpus (2)

• A classification of irreducible admissible mod p representations of p-adic reductive groups
• Existence of supersingular representations of p-adic reductive groups

Cited by in corpus (1)

• Restriction of $p$-modular representations of $U(2,1)$ to a Borel subgroup