Glasnik Matematicki, Vol. 59, No. 2 (2024), 351-405. \( \)

THE DEGENERATE PRINCIPAL SERIES REPRESENTATIONS OF EXCEPTIONAL GROUPS OF TYPE \(E_8\) OVER \(p\)-ADIC FIELDS

Hezi Halawi and Avner Segal

School of Mathematics, Ben Gurion University of the Negev, POB 653, Be'er Sheva 84105, Israel
e-mail:halawi@post.bgu.ac.il

Mathematics Department, Shamoon College of Engineering, 56 Bialik St., Beer-Sheva 84100, Israel
e-mail:avnerse@sce.ac.il

Abstract.   In this paper, we study the reducibility of degenerate principal series of the split, simple, simply-connected exceptional group of type \(E_8\). Furthermore, we calculate the maximal semi-simple subrepresentation and quotient of these representations for almost all cases.

2020 Mathematics Subject Classification.   22E50, 20G41, 20G05

Key words and phrases.   \(p\)-adic groups, degenerate principal series

Full text (PDF) (access from subscribing institutions only)

https://doi.org/10.3336/gm.59.2.06

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