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Types for tame p-adic groups

Publication ,  Journal Article
Fintzen, J
Published in: Annals of Mathematics
January 1, 2021

Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we show that every smooth irreducible complex representation of G(k) contains an s-type of the form constructed by Kim{ Yu and that every irreducible supercuspidal representation arises from Yu's construction. This improves an earlier result of Kim, which held only in characteristic zero and with a very large and ineffective bound on p. By contrast, our bound on p is explicit and tight, and our result holds in positive characteristic as well. Moreover, our approach is more explicit in extracting an input for Yu's construction from a given representation.

Duke Scholars

Published In

Annals of Mathematics

DOI

EISSN

1939-8980

ISSN

0003-486X

Publication Date

January 1, 2021

Volume

193

Issue

1

Start / End Page

303 / 346

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
MLA
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Fintzen, J. (2021). Types for tame p-adic groups. Annals of Mathematics, 193(1), 303–346. https://doi.org/10.4007/annals.2021.193.1.4
Fintzen, J. “Types for tame p-adic groups.” Annals of Mathematics 193, no. 1 (January 1, 2021): 303–46. https://doi.org/10.4007/annals.2021.193.1.4.
Fintzen J. Types for tame p-adic groups. Annals of Mathematics. 2021 Jan 1;193(1):303–46.
Fintzen, J. “Types for tame p-adic groups.” Annals of Mathematics, vol. 193, no. 1, Jan. 2021, pp. 303–46. Scopus, doi:10.4007/annals.2021.193.1.4.
Fintzen J. Types for tame p-adic groups. Annals of Mathematics. 2021 Jan 1;193(1):303–346.

Published In

Annals of Mathematics

DOI

EISSN

1939-8980

ISSN

0003-486X

Publication Date

January 1, 2021

Volume

193

Issue

1

Start / End Page

303 / 346

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics