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Representations of Lie algebras and partial differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Representations of Lie algebras and partial differential equationsby Xiaoping Xu.
Author:	Xu, Xiaoping.
Published:	Singapore :Springer Singapore :2017.
Description:	xxxvi, 620 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Lie algebras.
Online resource:	http://dx.doi.org/10.1007/978-981-10-6391-6
ISBN:	9789811063916$q(electronic bk.)

Representations of Lie algebras and partial differential equations
Xu, Xiaoping.

Representations of Lie algebras and partial differential equations[electronic resource] /by Xiaoping Xu. - Singapore :Springer Singapore :2017. - xxxvi, 620 p. :ill., digital ;24 cm.

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.

ISBN: 9789811063916$q(electronic bk.)

Standard No.: 10.1007/978-981-10-6391-6doiSubjects--Topical Terms:

191078
Lie algebras.

LC Class. No.: QA252.3 / .X8 2017

Dewey Class. No.: 512.482

Representations of Lie algebras and partial differential equations
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100 1 $a Xu, Xiaoping. $3 795011
245 1 0 $a Representations of Lie algebras and partial differential equations $h [electronic resource] / $c by Xiaoping Xu.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2017.
300 $a xxxvi, 620 p. : $b ill., digital ; $c 24 cm.
520 $a 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.
650 0 $a Lie algebras. $3 191078
650 0 $a Differential equations, Partial. $3 189753
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Algebra. $3 188312
650 2 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Special Functions. $3 274846
650 2 4 $a Algorithms. $3 184661
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856 4 0 $u http://dx.doi.org/10.1007/978-981-10-6391-6
950 $a Mathematics and Statistics (Springer-11649)