Asymptotics for singular vectors in Verma modules over the Virasoro algebra
type: Item
instance of: scholarly article
title: Asymptotics for singular vectors in Verma modules over the Virasoro algebra
zbMATH Open document ID: 0898.17012
author: M. García
published in: Pacific Journal of Mathematics
publication date: 1998-11-03T00:00:00Z
review text: Let \(M(h,c)\) be the Verma module over the Virasoro algebra with the highest weight \((h,c)\) and highest weight vector \(v\). For every \(k,l \in {\mathbb Z}\) and \(t \in {\mathbb C} \setminus 0\), let \[ h_{k,l}(t) = { {1-k^2} \over {4} } t+{ { 1-k l}\over {2} }+{ {1-l^2} \over {4} } t^{-1},\qquad c(t) = 6 t+13+6 t^{-1}. \] Then for \(k, l > 0\) and \(t \in {\mathbb C} \setminus 0\) the Verma module \(M( h_{k,l}(t), c(t))\) contains a singular vector \(S_{k,l} (t) v\) of degree \(k l\) [cf. \textit{D. Fuchs}, Adv. Sov. Math. 17, 65-74 (1993; Zbl 0827.17028)]. In the paper under review, the authors investigate the terms of extremal degrees of \(S_{k,l} (t)\). In particular, they prove that the highest and the lowest degrees of \(S_{k,l} (t)\) in \(t\) are equal, respectively, to \((k-1) l\) and \(-(l-1)k\).
reviewed by: Dražen Adamović
Mathematics Subject Classification ID: 17B68
zbMATH DE Number: 1054060
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: Verma modules
zbMATH Keywords: singular vectors
MaRDI profile type: Publication
full work available at URL: pjm.1997.177.201
OpenAlex ID: W2042477143
DOI: 10.2140/PJM.1997.177.201
description: scientific article; zbMATH DE number 1054060