# Representations Of Lie Algebras And Partial Differential Equations

by Xiaoping Xu /
2017 / English / EPUB

15.7 MB Download

This book provides explicit representations of finite-dimensional
simple Lie algebras, related partial differential equations,
linear orthogonal algebraic codes, combinatorics and algebraic
varieties, summarizing the author’s works and his joint works
with his former students. Further, it presents various
oscillator generalizations of the classical representation
theorem on harmonic polynomials, and highlights new functors from
the representation category of a simple Lie algebra to that of
another simple Lie algebra.

This book provides explicit representations of finite-dimensional
simple Lie algebras, related partial differential equations,
linear orthogonal algebraic codes, combinatorics and algebraic
varieties, summarizing the author’s works and his joint works
with his former students. Further, it presents various
oscillator generalizations of the classical representation
theorem on harmonic polynomials, and highlights new functors from
the representation category of a simple Lie algebra to that of
another simple Lie algebra.
Partial differential equations play a key role in solving certain
representation problems. The weight matrices of the minimal and
adjoint representations over the simple Lie algebras of types E
and F are proved to generate ternary orthogonal linear codes with
large minimal distances. New multi-variable hypergeometric
functions related to the root systems of simple Lie algebras are
introduced in connection with quantum many-body systems in one
dimension. In addition, the book identifies certain equivalent
combinatorial properties on representation formulas, and the
irreducibility of representations is proved directly related to
algebraic varieties. The book offers a valuable reference guide
for mathematicians and scientists alike. As it is largely
self-contained – readers need only a minimal background in
calculus and linear algebra – it can also be used as a
textbook.

Partial differential equations play a key role in solving certain
representation problems. The weight matrices of the minimal and
adjoint representations over the simple Lie algebras of types E
and F are proved to generate ternary orthogonal linear codes with
large minimal distances. New multi-variable hypergeometric
functions related to the root systems of simple Lie algebras are
introduced in connection with quantum many-body systems in one
dimension. In addition, the book identifies certain equivalent
combinatorial properties on representation formulas, and the
irreducibility of representations is proved directly related to
algebraic varieties. The book offers a valuable reference guide
for mathematicians and scientists alike. As it is largely
self-contained – readers need only a minimal background in
calculus and linear algebra – it can also be used as a
textbook.