Toda Orbits of Laguerre-polynomials and Representations of the Virasoro Algebra

Haine, Luc;Horozov, E.
(1993) Bulletin des sciences mathématiques — Vol. 117, n° 4, p. 485-518 (1993)

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  • Haine, LucUCLouvain
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  • Horozov, E.
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Abstract
We introduce partition functions Z(n)alpha (alpha > - 1, n = 0, 1, 2,...) which generate highest weight representations of the Virasoro algebra with highest weight (c, h) = (1, alpha2/4). These partition functions are tau-functions of Toda deformations of the generalized Laguerre polynomials, and for integer alpha they coincide with the partition functions of the rectangular matrix models.
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Haine, L., & Horozov, E. (1993). Toda Orbits of Laguerre-polynomials and Representations of the Virasoro Algebra. Bulletin des sciences mathématiques, 117(4), 485-518. https://hdl.handle.net/2078.5/69687 (Original work published 1993)