Subalgebras of $\gc_N$ and Jacobi polynomials

Details Subalgebras of $\gc_N$ and Jacobi polynomials Subalgebras of $\gc_N$ and Jacobi polynomials

2001-12-13

arxiv.org/abs/math-ph/0112028v1

Physics

Mathematical Physics

35 pages, LaTex

Scientific paper

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 $P_n^{(-\sigma,\sigma)}$, $\sigma\in\C$. 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.

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