10 citations · 23 across the 15 of their papers we have counts for
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Polynomial Representation of E6 and Its Combinatorial and PDE Implications
Xiaoping Xu
In this paper, we use partial differential equations to find the decomposition of the polynomial algebra over the basic irreducible module of E6 into a sum of irreducible submodule…
Polynomial Representation of and a New Combinatorial Identity about Twenty-Four
Xiaoping Xu
Singular vectors of a representation of a finite-dimensional simple Lie algebra are weight vectors in the underlying module that are nullified by positive root vectors. In this art…
Tree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations
Xiaoping Xu
A tree diagram is a tree with positive integral weight on each edge, which is a notion generalized from the Dynkin diagrams of finite-dimensional simple Lie algebras. We introduce…
Flag Partial Differential Equations and Representations of Lie Algebras
Xiaoping Xu
In this paper, we solve the initial value problems of variable-coefficient generalized wave equations associated with trees and a large family of linear constant-coefficient partia…