Explicit description of pro-p-Iwahori invariants of universal modules π_r for r=0 and q-1 via Iwahori-Hecke model, with algebra action determined, enabling functorial recovery and extension of Ollivier's theorem to other ramified extensions.
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For n greater than or equal to 3 and sufficiently generic weights, the universal supersingular representation of GL_n(k) is non-admissible and of infinite length.
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On the $I(1)$-invariants: Non-abelian Hecke algebra case
Explicit description of pro-p-Iwahori invariants of universal modules π_r for r=0 and q-1 via Iwahori-Hecke model, with algebra action determined, enabling functorial recovery and extension of Ollivier's theorem to other ramified extensions.
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Non-admissibility of some universal supersingular representations
For n greater than or equal to 3 and sufficiently generic weights, the universal supersingular representation of GL_n(k) is non-admissible and of infinite length.