Supercuspidal representations: An exhaustion theorem

By Ju-lee Kim. 2006

122 citations recorded by the source corpus.

Let be a reductive -adic group. We prove that all supercuspidal representations of arise through Yu's construction subject to certain hypotheses on (depending on ). As a corollary, under the same hypotheses, we see that any supercuspidal representation is compactly induced from a representation of an open subgroup which is compact modulo the center

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f9bd4746efaf2465b850643188bee8afec50d3e

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In Geometry and Topology

1. Tasho Kaletha
2. Mark Reeder
3. J. Yu
4. B. Gross
5. Shaun Stevens
6. Jessica Fintzen
7. W. Gan
8. Zhiwei Yun

In Mathematical Physics

1. Tasho Kaletha
2. Mark Reeder
3. J. Yu
4. B. Gross
5. Shaun Stevens
6. Jessica Fintzen
7. W. Gan
8. Zhiwei Yun

Citations in the corpus

• Epipelagic representations and invariant theory (2013, background): “(The generalization of Adler’s approach in [38] gives all supercuspidal representations of G(k) when p is large [20].”
• The supercuspidal representations of p-adic classical groups (2006, background): “Recently in [18], Kim has proved that, under some restrictive conditions on the ground field (dependent on the group G), Yu’s constructions do give all supercuspidal representations.”
• Arithmetic invariants of discrete Langlands parameters (2010, background): “For p large enough they appear in the constructions of [1] and [57], as they must, by [28].”
• Regular supercuspidal representations (2016, background): “When the residual characteristic of F is not too small for G the work of Kim [Kim07] shows that all supercuspidal representations of G(F ) arise from Yu’s construction.”