2 citations · 4 across the 4 of their papers we have counts for
18 papers
Etingof Trace, Path Hypergeometric Functions and Integrable Systems
Xiaoping Xu
Under a certain condition, we find the explicit formulas for the trace functions of certain intertwining operators among gl(n)-modules, introduced by Etingof in connection with the…
Representations of Centrally-Extended Lie Algebras over Differential Operators and Vertex Algebras
Xiaoping Xu
We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible m…
Differential Equations for Singular Vectors of sl(n)
Xiaoping Xu
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 Ver…
Construction of Gel'fand-Dorfman Bialgebras from Classical R-Matrices
Xiaoping Xu
Novikov algebras are algebras whose associators are left-symmetric and right multiplication operators are mutually commutative. A Gel'fand-Dorfman bialgebra is a vector space with…
Structure of Contact Lie Algebras Related to Locally-Finite Derivations
Yucai Su, Xiaoping Xu
Classical contact Lie algebras are the fundamental algebraic structures on the manifolds of contact elements of configuration spaces in classical mechanics. In this paper, we deter…
Nongraded Infinite-Dimensional Simple Lie Algebras
Xiaoping Xu
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play i…