Treffer: The Hidden Symmetry Algebras of a Class of Quasi-Exactly Solvable Multi Dimensional Operators: The hidden symmetry algebras of a class of quasi-exactly solvable multidimensional operators
Title:
The Hidden Symmetry Algebras of a Class of Quasi-Exactly Solvable Multi Dimensional Operators: The hidden symmetry algebras of a class of quasi-exactly solvable multidimensional operators
Authors:
Source:
Communications in Mathematical Physics. 196:445-459
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 1998.
Publication Year:
1998
Subject Terms:
Finite-dimensional groups and algebras motivated by physics and their representations, General mathematical topics and methods in quantum theory, Mathematics - Quantum Algebra, 0103 physical sciences, hidden symmetry, representations, FOS: Mathematics, Lie algebras and Lie superalgebras, Quantum Algebra (math.QA), matrix differential operators, 01 natural sciences, quasiexactly solvable equations
Document Type:
Fachzeitschrift
Article<br />Other literature type
File Description:
application/xml
ISSN:
1432-0916
0010-3616
0010-3616
DOI:
10.1007/s002200050430
DOI:
10.48550/arxiv.q-alg/9701016
Access URL:
http://arxiv.org/pdf/q-alg/9701016
http://arxiv.org/abs/q-alg/9701016
https://zbmath.org/1202579
https://doi.org/10.1007/s002200050430
https://arxiv.org/pdf/q-alg/9701016
https://arxiv.org/abs/q-alg/9701016
https://link.springer.com/article/10.1007/s002200050430
https://ui.adsabs.harvard.edu/abs/1998CMaPh.196..445B/abstract
https://link.springer.com/content/pdf/10.1007/s002200050430.pdf
http://arxiv.org/abs/q-alg/9701016
https://zbmath.org/1202579
https://doi.org/10.1007/s002200050430
https://arxiv.org/pdf/q-alg/9701016
https://arxiv.org/abs/q-alg/9701016
https://link.springer.com/article/10.1007/s002200050430
https://ui.adsabs.harvard.edu/abs/1998CMaPh.196..445B/abstract
https://link.springer.com/content/pdf/10.1007/s002200050430.pdf
Rights:
Springer TDM
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....6d0c8ce7ea4e5e61a9c5e5fea1d4f5b5
Database:
OpenAIRE
Weitere Informationen
Let $P(N,V)$ denote the vector space of polynomials of maximal degree less than or equal to $N$ in $V$ independent variables. This space is preserved by the enveloping algebra generated by a set of linear, differential operators representing the Lie algebra $gl(V+1)$. We establish the counterpart of this property for the vector space $P(M,V) \oplus P(N,V)$ for any values of the integers $M,N,V$. We show that the operators preserving $P(M,V) \oplus P(N,V)$ generate an abstract superalgebra (non linear if $��=\mid M-N\mid\geq 2$). A family of algebras is also constructed, extending this particular algebra by $��-1$ arbitrary complex parameters.
19 pages, latex