Representations of Lie Algebras and Partial Differential Equations

  title={Representations of Lie Algebras and Partial Differential Equations},
  author={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 partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties. Various oscillator generalizations of the classical representation theorem on harmonic polynomials are presented. New functors from the representation category of a simple Lie algebra to that of another simple Lie… 
5 Citations
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Cohomology of Oriented Tree Diagram Lie Algebras
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Tree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations
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Partial differential equation approach to F4
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Poisson vertex algebras in the theory of Hamiltonian equations
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Twisted Hamiltonian Lie algebras and their multiplicity-free representations
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It is known that many of the classes of simple Lie algebras of prime characteristic of nonclassical type have simple infinite-dimensional analogues of characteristic zero (see, for example, [4, p.
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