The character of the Weil representation of a finite abelian group of odd order

Autor:	Ladisch, Frieder
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory Mathematics - Group Theory Mathematics - Number Theory 11F27 (Primary) 20C15 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Let $V$ be a finite abelian group of odd order, equipped with a non-degenerate, alternating form $\omega\colon V\times V \to \mathbb{Z}/m\mathbb{Z}$. We give closed formulas for the character values of the Weil representation associated with $(V,\omega)$. These formulas generalize the ones given by S. Gurevich and R. Hadani (2007) and by T. Thomas (2008, 2013) from finite vector spaces to abelian groups. Our formulas do not involve the choice of a Lagrangian subgroup of $V$. Our proofs are based on an elementary algebraic approach introduced by H. N. Ward (1972, 2017) for finite vector spaces over fields. Comment: 36 pages; latex, bibliography with biblatex
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.09676 Zobrazit plný text záznamu View this record from Arxiv