arXiv subjects

Prem Dagar

Publications and source records attributed to Prem Dagar.

3 recordsLinked to original sources

arXiv2026

On representations of GL(n) distinguished by GL(1)*GL(n-1) over a quaternion division algebra

Let $D$ be a quaternion division algebra over a non-Archimedean local field $F$ of characteristic zero, and let $G_n=GL_n(D)$. Let $H_{1,n-1}$ denote the subgroup of $G_n$ consisting of block-diagonal matrices of the form $diag(g_1,g_2)$, where $g_1\in G_1$ and $g_2\in G_{n-1}$. In this article, we formulate a conjectural classification of irreducible smooth $H_{1,n-1}$-distinguished representations of $G_n$ for $n>2$. We prove this conjecture in the cases $n=3$ and $n=4$. When $n=2$, the results are well known due to the contributions by various authors.

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arXiv2024

On the Jacquet functor of Symplectic groups

We prove that, for an equivalence class of irreducible smooth representations of the symplectic group Sp(2n,F) over a non-Archimedean local field F, the Jacquet functor with respect to the maximal Levi subgroup GL(l,F)\times Sp(2n-2l,F) is multiplicity-free. The proof is based on an explicit computation of Jacquet modules for a broader family of Sp(2n,F)-representations induced from segments, yielding a detailed structural description that may be of independent interest.

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arXiv2024

A note on Jacquet modules of general linear groups

Let F be a non-Archimedean local field. Consider G_n:= GL_n(F) and let M:= G_l * G_{n-l} be a maximal Levi subgroup of G_n. In this article, we compute the semisimplified Jacquet module of representations of G_n with respect to the maximal Levi subgroup M, belonging to a particular category of representations. Utilizing our results, we prove that the Jacquet module is multiplicity-free for a specific subcategory of representations. Our findings are based on the Zelevinsky classification.

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