Quantum algebra Uq(gl(3)) and nonlinear optics

被引：1

作者：

Gruber, B ^{[1
]}

Smirnov, YF

Kharitonov, YI

机构：

[1] So Illinois Univ, Carbondale, IL 62901 USA

[2] Moscow MV Lomonosov State Univ, DV Skobeltsyn Inst Nucl Phys, Moscow 119899, Russia

[3] Russian Acad Sci, St Petersburg Inst Nucl Phys, Gatchina 188350, Russia

来源：

JOURNAL OF RUSSIAN LASER RESEARCH | 2003年 / 24卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

nonlinear optics; quantum groups; indecomposable representations;

D O I：

10.1023/A:1022569409239

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

Indecomposable representations are investigated for the U-q(gl(3)) quantum algebra. The matrix elements are explicitly determined for the elementary representation is and the extremal vectors which characterize invariant subspaces are given in explicit form. Quotient spaces are used to derive other representations from the elementary representations. including the finite-dimensional irreducible representations and infinite-dimensional representations which are bounded above. Applications to nonlinear-optical phenomena are discussed.

引用

页码：56 / 68

页数：13

共 25 条

[1]

Bernstein I.N, 1971, FUNKC ANAL PRILOZH, V5, P1, DOI 10.1007/BF01075841

[2] A REMARKABLE REPRESENTATION OF 3 + 2 DE SITTER GROUP [J].