Differential equations and singular vectors in Verma modules over sl( n , ℂ)
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| 024 | 7 | 0 | |a 10.1007/s10114-015-4640-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4640-7 | ||
| 100 | 1 | |a Xiao |D Wei |u College of Mathematics and Computational Science, Shenzhen University, 518060, Shenzhen, P. R. China |4 aut | |
| 245 | 1 | 0 | |a Differential equations and singular vectors in Verma modules over sl( n , ℂ) |h [Elektronische Daten] |c [Wei Xiao] |
| 520 | 3 | |a Xu introduced a system of partial differential equations to investigate singular vectors in the Verma module of highest weight λ over sl(n,ℂ). He gave a differential-operator representation of the symmetric group S n on the corresponding space of truncated power series and proved that the solution space of the system is spanned by {σ(1) | σ ∈ S n }. It is known that S n is also the Weyl group of sl(n,ℂ) and generated by all reflections s α with positive roots α. We present an explicit formula of the solution s α(1) for every positive root α and show directly that s α(1) is a polynomial if and only if 〈λ + ρ, α〉 is a nonnegative integer. From this, we can recover a formula of singular vectors given by Malikov et al.. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Verma modules |2 nationallicence | |
| 690 | 7 | |a singular vector |2 nationallicence | |
| 690 | 7 | |a differential equation |2 nationallicence | |
| 690 | 7 | |a truncated power series |2 nationallicence | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/7(2015-07-01), 1057-1066 |x 1439-8516 |q 31:7<1057 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4640-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4640-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Xiao |D Wei |u College of Mathematics and Computational Science, Shenzhen University, 518060, Shenzhen, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/7(2015-07-01), 1057-1066 |x 1439-8516 |q 31:7<1057 |1 2015 |2 31 |o 10114 | ||