Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 2, pp. 205-236
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We give a uniform interpretation of the classical continuous Chebyshev and Hahn orthogonal polynomials of a discrete variable in terms of the Feigin Lie algebra $\mathfrak{gl}(\lambda)$ for $\lambda\in\mathbb C$. The Chebyshev and Hahn $q$-polynomials admit a similar interpretation, and orthogonal polynomials corresponding to Lie superalgebras can be introduced. We also describe quasi-finite modules over $\mathfrak{gl}(\lambda)$, real forms of this algebra, and the unitarity conditions for quasi-finite modules. Analogues of tensors over $\mathfrak{gl}(\lambda)$ are also introduced.
@article{TMF_2000_123_2_a5,
author = {D. A. Leites and A. N. Sergeev},
title = {Orthogonal polynomials of a discrete variable and {Lie} algebras of complex-size matrices},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {205--236},
publisher = {mathdoc},
volume = {123},
number = {2},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a5/}
}
TY - JOUR AU - D. A. Leites AU - A. N. Sergeev TI - Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2000 SP - 205 EP - 236 VL - 123 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a5/ LA - ru ID - TMF_2000_123_2_a5 ER -
%0 Journal Article %A D. A. Leites %A A. N. Sergeev %T Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices %J Teoretičeskaâ i matematičeskaâ fizika %D 2000 %P 205-236 %V 123 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a5/ %G ru %F TMF_2000_123_2_a5
D. A. Leites; A. N. Sergeev. Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 2, pp. 205-236. http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a5/