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Bernstein center of supercuspidal blocks

Manish Mishra


Let 𝐆 be a tamely ramified connected reductive group defined over a non-archimedean local field k. We show that the Bernstein center of a tame supercuspidal block of 𝐆(k) is isomorphic to the Bernstein center of a depth-zero supercuspidal block of 𝐆0(k) for some twisted Levi subgroup of 𝐆0 of 𝐆.


The author is very thankful to Rainer Weissauer, Jeff Adler, Sandeep Varma and David Kazhdan for many helpful interactions. He is especially grateful to Jiu-Kang Yu for his careful proof reading and making important suggestions. He is also thankful to the Math Institute at Heidelberg University for supporting his stay during which this work was written.


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Received: 2015-12-22
Revised: 2016-02-12
Published Online: 2016-08-11
Published in Print: 2019-03-01

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