Differential Equations for Singular Vectors of sl(n)

2003/05/13 by Xiaoping Xu, Xu, Xiaoping · 1 citation
Mathematics · #17B69 #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.AP #math.QA #math.RT #msc:17B69

paper · pdf · doi:10.48550/arxiv.math/0305180

25pages

arxiv created 2003/05/13 · arxiv updated 2009/11/30

Abstract

Given a weight of sl(n), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module. Moreover, we completely solve the system in a certain space of power series. The polynomial solutions correspond to the singular vectors in the Verma module. The well-known results of Verma, Bernstein-Gel'fand-Gel'fand and Jantzen for the case of sl(n) are naturally included in our almost elementary approach of partial differential equations.

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• Differential-Operator Representations of S_n and Singular Vectors in Verma Modules

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