## Square integrable representations of classical p-adic groups corresponding to segments

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- by Marko Tadić
- Represent. Theory
**3**(1999), 58-89 - DOI: https://doi.org/10.1090/S1088-4165-99-00071-0
- Published electronically: June 9, 1999
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## Abstract:

Let $S_n$ be either the group $Sp(n)$ or $SO(2n+1)$ over a $p$-adic field $F$. Then Levi factors of maximal parabolic subgroups are (isomorphic to) direct products of $GL(k)$ and $S_{n-k}$, with $1\leq k\leq n$. The square integrable representations which we define and study in this paper (and prove their square integrability), are subquotients of reducible representations Ind$_P^{S_n}(\delta \otimes \sigma ),$ where $\delta$ is an essentially square integrable representation of $GL(k)$, and $\sigma$ is a cuspidal representation of $S_{n-k}$. These square integrable representations play an important role in a construction of more general square integrable representations.## References

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## Bibliographic Information

**Marko Tadić**- Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
- ORCID: 0000-0002-6087-3765
- Email: tadic@math.hr
- Received by editor(s): July 17, 1998
- Received by editor(s) in revised form: December 6, 1998
- Published electronically: June 9, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Represent. Theory
**3**(1999), 58-89 - MSC (1991): Primary 22E50
- DOI: https://doi.org/10.1090/S1088-4165-99-00071-0
- MathSciNet review: 1698200