“Degenerate representations of $GL_n$ over a p-adic field”
Giovedì 9 Gennaio 2025, ore 14:30 - Sala riunioni 7B1 - Johannes Girsch (University of Sheffield)
Abstract
Smooth generic representations of $GL_n$ over a p-adic field $F$, i.e. representations admitting a non-degenerate Whittaker model, are an important class of representations, for example in the setting of Rankin-Selberg integrals. However, in recent years there has been an increased interest in non-generic representations and their degenerate Whittaker models. By the theory of Bernstein-Zelevinsky derivatives we can associate to each smooth irreducible representation of $GL_n(F)$ an integer partition of $n$, which encodes the “degeneracy” of the representation. By using these “highest derivative partitions” we can define a stratification of the category of smooth complex representations and prove the surprising fact that all of the strata categories are equivalent to module categories over commutative rings.
This is joint work with David Helm.
