ﻻ يوجد ملخص باللغة العربية
We show that near a point where the equilibrium density of eigenvalues of a matrix model behaves like y ~ x^{p/q}, the correlation functions of a random matrix, are, to leading order in the appropriate scaling, given by determinants of the universal (p,q)-minimal models kernels. Those (p,q) kernels are written in terms of functions solutions of a linear equation of order q, with polynomial coefficients of degree at most p. For example, near a regular edge y ~ x^{1/2}, the (1,2) kernel is the Airy kernel and we recover the Airy law. Those kernels are associated to the (p,q) minimal model, i.e. the (p,q) reduction of the KP hierarchy solution of the string equation. Here we consider only the 1-matrix model, for which q=2.
n-ary algebras have played important roles in mathematics and mathematical physics. The purpose of this paper is to construct a deformation of Virasoro-Witt n-algebra based on an oscillator realization with two independent parameters (p, q) and investigate its n-Lie subalgebra.
There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are
We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group $U_q(mathcal L(m
We show that Liouville gravity arises as the limit of pure Einstein gravity in 2+epsilon dimensions as epsilon goes to zero, provided Newtons constant scales with epsilon. Our procedure - spherical reduction, dualization, limit, dualizing back - pass
Motivated by the universal knot polynomials in the gauge Chern-Simons theory, we show that the values of the second Casimir operator on an arbitrary power of Cartan product of $X_2$ and adjoint representations of simple Lie algebras can be represente