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Glasnik matematički, Vol. 59 No. 2, 2024.

Izvorni znanstveni članak

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

The degenerate principal series representations of exceptional groups of type \(E_8\) over \(p\)-adic fields

Hezi Halawi ; School of Mathematics, Ben Gurion University of the Negev, POB 653, Be'er Sheva 84105, Israel
Avner Segal ; Mathematics Department, Shamoon College of Engineering, 56 Bialik St., Beer-Sheva 84100, Israel

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str. 351-405

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Sažetak

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.

Ključne riječi

\(p\)-adic groups, degenerate principal series

Hrčak ID:

325175

URI

https://hrcak.srce.hr/325175

Datum izdavanja:

28.12.2024.

Posjeta: 0 *

Publication date: 15 December 2024

Volume: Vol 59

Issue: Svezak 2

Pages: 351-405

DOI: 10.3336/gm.59.2.06

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: \(p\)-adic groups, degenerate principal series

The degenerate principal series representations of exceptional groups of type \(E_8\) over \(p\)-adic fields

Hezi Halawi[1]

Email: halawi@post.bgu.ac.il

Avner Segal[2]

Email: avnerse@sce.ac.il

 

[1] School of Mathematics, Ben Gurion University of the Negev, POB 653, Be'er Sheva 84105, Israel

[2] Mathematics Department, Shamoon College of Engineering, 56 Bialik St., Beer-Sheva 84100, Israel

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.

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