Geodesic
Subalgebras of gcN and Jacobi Polynomials
Canadian mathematical bulletin, Tome 45 (2002) no. 4, pp. 567-605

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DOI

We classify the subalgebras of the general Lie conformal algebra $\text{g}{{\text{c}}_{N}}$ that act irreducibly on $\mathbb{C}\,{{\left[ \partial\right]}^{N}}$ and that are normalized by the $\text{s}{{\text{l}}_{2}}$ -part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials $P_{n}^{\left( -\sigma ,\sigma\right)}$ , $\sigma \,\in \,C$ . The connection goes both ways—we use in our classification some classical properties of Jacobi polynomials, and we derive from the theory of conformal algebras some apparently new properties of Jacobi polynomials.
DOI : 10.4153/CMB-2002-055-9
Mots-clés : 17B65, 17B68, 17B69, 33C45 
Sole, Alberto De; Kac, Victor G. Subalgebras of gcN and Jacobi Polynomials. Canadian mathematical bulletin, Tome 45 (2002) no. 4, pp. 567-605. doi: 10.4153/CMB-2002-055-9
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     title = {Subalgebras of {gcN} and {Jacobi} {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {567--605},
     year = {2002},
     volume = {45},
     number = {4},
     doi = {10.4153/CMB-2002-055-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-055-9/}
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