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Toda orbits of Laguerre polynomials and representations of the Virasoro algebra. (English) Zbl 0831.17011
Authors’ abstract: We introduce partition functions \(Z_n^\alpha\) \((\alpha> -1\), \(n= 0, 1, 2, \dots)\) which generate highest weight representations of the Virasoro algebra with highest weight \((c, h)= (1, \alpha^2/ 4)\). These partition functions are tau-functions of Toda deformations of the generalized Laguerre polynomials, and for integral \(\alpha\) they coincide with the partition function of the rectangular matrix models.
Reviewer: H.Yamada (Tokyo)

17B68 Virasoro and related algebras
35Q58 Other completely integrable PDE (MSC2000)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
81T20 Quantum field theory on curved space or space-time backgrounds