Mathematics

Findings from Institute of Mathematics Advance Knowledge in Mathematical Theories

  2012 APR 17 - (VerticalNews.com) -- According to the authors of a study from Beijing, People's Republic of China, "Given a weight of sl(n, C), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module, and a differential-operator representation of the symmetric group Sn on the related space of truncated power series."

  "We prove that the solution space of the system of partial differential equations is exactly spanned by {sigma(1) | sigma is an element of S-n}. Moreover, the singular vectors of sl(n, C) in the Verma module are given by those sigma(1) that are polynomials," wrote X.P. Xu and colleagues, Institute of Mathematics.

  The researchers concluded: "The well-known results of Verma, Bernstein-Gel'fand-Gel'fand and Jantzen for the case of sl(n, C) are naturally included in our almost elementary approach of partial differential equations."

  Xu and colleagues published their study in Algebras and Representation Theory (Differential-Operator Representations of S-n and Singular Vectors in Verma Modules. Algebras and Representation Theory, 2012;15(2):211-231).

  For more information, contact X.P. Xu, Chinese Academy Sci, Academy Math & Syst Sci, Inst Math, Hua Loo Keng Key Math Lab, Beijing 100190, People's Republic of China.

  Publisher contact information for the journal Algebras and Representation Theory is: Springer, Van Godewijckstraat 30, 3311 Gz Dordrecht, Netherlands.

  Keywords: City:Beijing, Country:People's Republic of China, Region:Asia, Mathematical Theories

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2012, VerticalNews Mathematics via VerticalNews.com.