# Representations of Lie Algebras and Partial Differential Equations

@inproceedings{Xu2017RepresentationsOL, title={Representations of Lie Algebras and Partial Differential Equations}, author={Xiaoping Xu}, year={2017} }

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

An overview of generalised Kac-Moody algebras on compact real manifolds

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Projective oscillator representations of and

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- 2021

Abstract Motivated from understanding higher-dimensional supersymmetric conformal field theory, we study various inhomogeneous oscillator representations of and on supersymmetric polynomial algebras…

Irreducible $W_n^+$-modules from Weyl modules and $\mathfrak{gl}_{n}$-modules

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- 2016

For an irreducible module $P$ over the Weyl algebra $\mathcal{K}_n^+$ (resp. $\mathcal{K}_n$) and an irreducible module $M$ over the general liner Lie algebra $\mathfrak{gl}_n$, using Shen's…

Thermal effect on primordial black holes in standard Higgs minimum double-well potential

- Physics
- 2019

We attempt a new scheme to combine the Higgs field in the minimal standard model and the statistic physics with thermal effect together. By introducing the stochastic differential equation in FRW…

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