Non-cuspidality outside the middle degree of l-adic cohomology of the Lubin-Tate tower

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162255In this article, we consider the representations of the general linear group over a non-archimedean local field obtained from the vanishing cycle cohomology of the Lubin-Tate tower. We give an easy and direct proof of the fact that no supercuspidal representation appears as a subquotient of such representations unless they are obtained from the cohomology of the middle degree. Our proof is purely local and does not require Shimura varieties.12 pagesRepresentation TheoryAlgebraic Geometry22E50; 14G35; 11F70Non-cuspidality outside the middle degree of l-adic cohomology of the Lubin-Tate towertext