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Representation Theory

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Degenerate principal series for classical and odd GSpin groups in the general case

Authors: Yeansu Kim, Baiying Liu and Ivan Matić
Journal: Represent. Theory 24 (2020), 403-434
MSC (2010): Primary 22E35; Secondary 22E50, 11F70
Published electronically: August 26, 2020
MathSciNet review: 4139900
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Abstract: Let $G_n$ denote either the group $SO(2n+1, F)$, $Sp(2n, F)$, or $G{\mathrm {Spin}}(2n+1, F)$ over a non-archimedean local field of characteristic different from two. We determine all composition factors of degenerate principal series of $G_n$, using methods based on the Aubert involution and known results on irreducible subquotients of the generalized principal series of a particular type.

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Additional Information

Yeansu Kim
Affiliation: Department of Mathematics Education, Chonnam National University, 77 Yongbong-ro, Buk-gu, Gwangju city, South Korea
MR Author ID: 1094118
ORCID: 0000-0001-9427-6136

Baiying Liu
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
MR Author ID: 953254

Ivan Matić
Affiliation: Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia
MR Author ID: 779049
ORCID: 0000-0001-9264-9293

Keywords: Classical $p$-adic groups, degenerate principal series, generalized principal series
Received by editor(s): July 6, 2019
Received by editor(s) in revised form: February 22, 2020
Published electronically: August 26, 2020
Additional Notes: The first author was supported by Chonnam National University (Grant number: 2018-0978).
The second author was partially supported by NSF grants DMS-1702218, DMS-1848058, and by start-up funds from the Department of Mathematics at Purdue University.
The third author was partially supported by Croatian Science Foundation under the project IP-2018-01-3628.
Article copyright: © Copyright 2020 American Mathematical Society