On degenerate Whittaker space for $GL_4(\mathfrak{o}_2)$ (2407.21165v1)

Abstract: Let $\mathfrak{o}2$ be a finite principal ideal local ring of length 2. For a representation $\pi$ of $GL{4}(\mathfrak{o}2)$, the degenerate Whittaker space $\pi{N, \psi}$ is a representation of $GL_2(\mathfrak{o}2)$. We describe $\pi{N, \psi}$ explicitly for an irreducible strongly cuspidal representation $\pi$ of $GL_4(\mathfrak{o}2)$. This description verifies a special case of a conjecture of Prasad. We also prove that $\pi{N, \psi}$ is a multiplicity free representation.