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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.