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Differential Equations for Singular Vectors of sl(n) | | Xiaoping Xu
; | | Date: |
13 May 2003 | | Subject: | Quantum Algebra; Analysis of PDEs; Representation Theory MSC-class: 17B69 | math.QA math.AP math.RT | | 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. | | Source: | arXiv, math.QA/0305180 | | Services: | Forum | Review | PDF | Favorites | |
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