Subalgebras of $\gc_N$ and Jacobi polynomials

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 ${\mathrm{sl}}_2$--part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials $P_n^{(-\sigma ,\sigma )}$, $σ\in\C$. 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.

35 pages, LaTex

References in corpus (1)

• Extensions of conformal modules

Cited by in corpus (7)

• Low dimensional cohomology of general conformal algebras $g{c}_N$
• Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras
• Simple associative conformal algebras of linear growth
• Classification of finite irreducible conformal modules over a class of Lie conformal algebras of Block type
• On a class of infinite simple Lie conformal algebras
• Simplicity of quadratic Lie conformal algebras
• Associative conformal algebras with finite faithful representation