Depth-zero supercuspidal L-packets and their stability

By Stephen Debacker, Mark Reeder. 2009

164 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c8568c1c57ba9d77a0046fc54b76b40def1b4436

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In Geometry and Topology

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

In Mathematical Physics

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

Citations in the corpus

• Arithmetic invariants of discrete Langlands parameters (2010, background): “For example, the correspondence discussed in [10] and [21] involves H(k,G0), which parametrizes the pure inner forms of the quasi-split group G0.”
• Rigid inner forms of real and p-adic groups (2013, background): “s formulation the top arrow is expected to be bijective both in the real and in the p-adic case, makingthisformulationmoreuniformthanthatof(1.1). Thediagram(1.2)was constructed by DeBacker and Reeder [DR09] for any unramified p-adic group Gandaclassofdepth-zerosupercuspidalLanglandsparametersϕ. Itwas”
• Epipelagic representations and invariant theory (2013, methodology): “The latter was used in [10] to construct L-packets of depth-zero supercuspidal representations of p-adic groups, along with their Langlands parameters, under the (still conjectural) local Langlands correspondence.”
• Genericity and contragredience in the local Langlands correspondence (2012, methodology): “For general connected reductive groups, there are constructions of the correspondence for specific classes of parameters, including the classical case of unramified representations, the case of representations with Iwahori-fixed vector by work of Kazhdan–Lusztig, unipotent representations by work of”
• Generalizations of the Springer correspondence and cuspidal Langlands parameters (2015, unknown): “ H∨ is a torus. The latter condition forces φto be trivial on SL2(C). Hence uφ = 1, and any enhancement of φgives a cuspidal L-parameter. Let Cφ = π0 ZH∨(φ)/Z(LH)◦ and let ρ∈Irr(Cφ). It is known from [DeRe] that these enhanced L-parameters (φ,ρ) correspond to the depth-zero generic supercuspidal irr”
• Epipelagic $$L$$L-packets and rectifying characters (2012, methodology): “Acknowledgments This work has profited greatly from enlightening and inspiring mathematical conversations with Stephen DeBacker, Benedict Gross, Guy Henniart, Atsushi Ichino, Robert Kottwitz, Mark Reeder, and Loren Spice.”
• Restrictions of representations of classical groups: examples (2009, unknown): “of these characters are tamely ramified: f(αi) = f(βj) = 1. The L-packet Πϕof depth zero supercuspidal representations of the pure inner forms G= U(W)×U(W0) has been constructed by DeBacker and Reeder [DR], and we briefly RESTRICTION PROBLEMS FOR CLASSICAL GROUPS 7 summarize their results in this case”