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On the Unicity of Types for Toral Supercuspidal Representations

  • Peter Latham
  • Monica NevinsEmail author
Chapter
Part of the Progress in Mathematics book series (PM, volume 328)

Abstract

For tame arbitrary-length toral, also called positive regular, supercuspidal representations of a simply connected and semisimple p-adic group G, constructed as per Adler-Yu, we determine which components of their restriction to a maximal compact subgroup are types. We give conditions under which there is a unique such component and then present a class of examples for which there is not, disproving the strong version of the conjecture of unicity of types on maximal compact open subgroups. We restate the unicity conjecture and prove it holds for the groups and representations under consideration under a mild condition on depth.

Notes

Acknowledgements

The second author warmly thanks Anne-Marie Aubert, Manish Mishra, Alan Roche and Steven Spallone for the invitation to the excellent conference Representation theory of p-adic groups at IISER Pune, India. The stimulating environment of the workshop contributed significantly to this article; in particular, fellow participant Jeff Adler provided invaluable insight into tori and buildings, and he offered up the torus of Example 8.2.

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsKing’s College LondonLondonUK
  2. 2.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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