Glasnik Matematicki, Vol. 59, No. 1 (2024), 77-105. \( \)

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
e-mail:igor.ciganovic@math.hr

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 \(\frac{1}{2}\leq a < b < c\), \(\rho\) 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.

2020 Mathematics Subject Classification.   22D30, 22E50, 22D12, 11F85

Key words and phrases.   Classical group, composition series, induced representations, \(p\)-adic field, Jacquet module

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

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