We classify the subalgebras of the general Lie conformal algebra gc_N that act irreducibly on C[d]^N and that are normalized by the sl_2-part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials. The connection goes both ways : we use in our classication some classical properties of Jacobi polynomials, and we derive from the theory of conformal algebras some apparently new properties of Jacobi polynomials.
Subalgebras of gc_N and Jacobi polynomials / DE SOLE, Alberto; Kac, V.. - In: CANADIAN MATHEMATICAL BULLETIN. - ISSN 0008-4395. - STAMPA. - 45:4(2002), pp. 567-605.
Subalgebras of gc_N and Jacobi polynomials
DE SOLE, ALBERTO;
2002
Abstract
We classify the subalgebras of the general Lie conformal algebra gc_N that act irreducibly on C[d]^N and that are normalized by the sl_2-part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials. The connection goes both ways : we use in our classication some classical properties of Jacobi polynomials, and we derive from the theory of conformal algebras some apparently new properties of Jacobi polynomials.File allegati a questo prodotto
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