IRREDUCIBLE REPRESENTATIONS OF AN ALGEBRA UNDERLYING HIDDEN SYMMETRIES OF A CLASS OF QUASI EXACTLY SOLVABLE SYSTEMS OF EQUATIONS

Authors
BRIHAYE Y GILLER S KOSINSKI P NUYTS J
Citation
Y. Brihaye et al., IRREDUCIBLE REPRESENTATIONS OF AN ALGEBRA UNDERLYING HIDDEN SYMMETRIES OF A CLASS OF QUASI EXACTLY SOLVABLE SYSTEMS OF EQUATIONS, Communications in Mathematical Physics, 187(1), 1997, pp. 201-226
Citations number
11
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
187
Issue
1
Year of publication
1997
Pages
201 - 226
Database
ISI
SICI code
0010-3616(1997)187:1<201:IROAAU>2.0.ZU;2-M
Abstract
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n - 2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional representations of this algebra are classified int o five infinite discrete sets and one exceptional case. Their matrix e lements are given explicitly. The results are related to the theory of quasi exactly solvable equations.