Original scientific paper

https://doi.org/10.3336/gm.59.1.04

Parabolic induction from two segments, linked under contragredient, with a one half cuspidal reducibility, a special case

Igor Ciganović ; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia

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Abstract

In this paper, we determine the composition series of the induced representation
\(\delta([\nu^{-a}\rho,\nu^c\rho])\times \delta([\nu^\frac{1}{2}\rho,\nu^b\rho])\rtimes \sigma\) where
\(a, b, c \in \mathbb{Z}+\frac{1}{2}\) such that \(\frac{1}{2}\leq a \le b \le c\),
\(\rho\) is an irreducible cuspidal unitary representation of a general linear group
and \(\sigma\) is an irreducible cuspidal representation of a classical group such that
\(\nu^\frac{1}{2}\rho\rtimes \sigma\) reduces.

Keywords

Classical group, composition series, induced representations, \(p\)-adic field, Jacquet module

Hrčak ID:

318151

URI

https://hrcak.srce.hr/318151

Publication date:

30.6.2024.

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