10 citations · 65 across the 48 of their papers we have counts for
48 papers
Full Conformal Oscillator Representations of Orthogonal Lie Algebras and Combinatorial Identities
Zhenyu Zhou, Xiaoping Xu
Zhao and the second author (2013) constructed a functor from o(k)-Mod to o(k + 2)-Mod. In this paper, we use the functor successively to obtain an universal first-order differentia…
Full Projective Oscillator Representations of Special Linear Lie Algebras and Combinatorial Identities
Zhenyu Zhou, Xiaoping Xu
Using the projective oscillator representation of sl(n+1) and Shen's mixed product for Witt algebras, Zhao and the second author (2011) constructed a new functor from sl(n)-Mod to…
Representations of Lie Algebras and Partial Differential Equations
Xiaoping Xu
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related…
Conformal Oscillator Representations of Orthogonal Lie Algebras
Xiaoping Xu
The conformal transformations with respect to the metric defining the orthogonal Lie algebra o(n) give rise to a one-parameter (c) family of inhomogeneous first-order differential…
Projective Oscillator Representations of sl(n+1) and sp(2m+2)
Xiaoping Xu
The n-dimensional projective group gives rise to a one-parameter family of inhomogeneous first-order differential operator representations of sl(n+1). By partially swapping differe…
Moving-Frame Approach to Nonlinear Internal Waves in Oceans
Xiaoping Xu
In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solu…