Symplectic model for Zelevinsky modules of GL(n,D)
Representation Theory
2026-03-02 v1
Abstract
Let D be a quaternion division algebra over a non-archimedean local field F of characteristic zero. This article demonstrates the existence and uniqueness of the symplectic model for a family of Zelevinsky modules of GL(n, D) to a family of irreducible representations of GL(n, D). For this family of irreducible representations, we identify a necessary condition under which a symplectic model can exist. This work extends a result of Offen and Sayag beyond the case D = F.
Keywords
Cite
@article{arxiv.2602.23917,
title = {Symplectic model for Zelevinsky modules of GL(n,D)},
author = {Hariom Sharma},
journal= {arXiv preprint arXiv:2602.23917},
year = {2026}
}
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9 pages