Talk
Speaker: Hariom Sharma, IIT Bombay
Host: Ravi Raghunathan
Title: Symplectic Model for Zelevinsky Modules of GL(n, D)
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, August 14
Venue: Ramanujan Hall
Abstract: Let D be a quaternion division algebra over a non-Archimedean local field F of characteristic zero. Let m = (Δ₁,..., Δₖ) be a well-ordered multisegment, and let π(m) = Z(Δ₁) × ··· × Z(Δₖ) be the associated Zelevinsky module of GL(n, D). In this talk, we study the existence and uniqueness of symplectic models for Zelevinsky modules. Under the assumption that no representation occurring in the cuspidal support of m admits a symplectic model, we prove that π(m) admits a symplectic model if and only if every segment in m has even length. We further show that, whenever such a model exists, it is unique. As a consequence, if the unique irreducible quotient Z(m) of π(m) admits a symplectic model, then every segment in m has even length.