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Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups

Chris Jantzen University of Chicago, Chicago, IL
Available Formats:
Electronic ISBN: 978-1-4704-0175-7
Product Code: MEMO/124/590.E
List Price: $44.00 MAA Member Price:$39.60
AMS Member Price: $26.40 Click above image for expanded view Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups Chris Jantzen University of Chicago, Chicago, IL Available Formats:  Electronic ISBN: 978-1-4704-0175-7 Product Code: MEMO/124/590.E  List Price:$44.00 MAA Member Price: $39.60 AMS Member Price:$26.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 1241996; 100 pp
MSC: Primary 22;

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.

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

• Chapters
• 1. Introduction
• 2. Notation and preliminaries
• 3. Components: Useful special cases
• 4. Reducibility points
• 5. Components: The “ramified” case
• 6. Components: The “unramified” case
• 7. Composition series
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 1241996; 100 pp
MSC: Primary 22;

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.

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

• Chapters
• 1. Introduction
• 2. Notation and preliminaries
• 3. Components: Useful special cases
• 4. Reducibility points
• 5. Components: The “ramified” case
• 6. Components: The “unramified” case
• 7. Composition series
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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