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Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups
Chris Jantzen, University of Chicago, IL
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Memoirs of the American Mathematical Society
1996; 100 pp; softcover
Volume: 124
ISBN-10: 0-8218-0482-0
ISBN-13: 978-0-8218-0482-7
List Price: US$41
Individual Members: US$24.60
Institutional Members: US$32.80
Order Code: MEMO/124/590
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This memoir studies reducibility in a certain class of induced representations for \(Sp_{2n}(F)\) and \(SO_{2n+1}(F)\), where \(F\) is \(p\)-adic. In particular, it is concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadić, the reducibility points for such representations are determined. When reducible, the composition series is described, giving Langlands data and Jacquet modules for the irreducible composition factors.

Readership

Graduate students and research mathematicians interested in topological groups, Lie groups.

Table of Contents

  • Introduction
  • Notation and preliminaries
  • Components: useful special cases
  • Reducibility points
  • Components: the "ramified" case
  • Components: the "unramified" case
  • Composition series
  • References
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