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Subalgebras of $\gc_N$ and Jacobi polynomials

Alberto De Sole·Victor G. Kac
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Abstract

We classify the subalgebras of the general Lie conformal algebra $\gc_N$ that act irreducibly on $\C[\partial]^N$ and that are normalized by the $\operatorname{sl}_2$--part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials $P_n^{(-σ,σ)}$, $σ\in\C$. 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.

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Alberto De Sole, Victor G. Kac. 2001-12-13. Subalgebras of $\gc_N$ and Jacobi polynomials. https://doi.org/10.4153/cmb-2002-055-9

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