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Towards construction of superintegrable basis in matrix models
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Towards construction of superintegrable basis in matrix models
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We develop methods for systematic construction of superintegrable polynomials in matrix/eigenvalue models. Our consideration is based on a tight connection of superintegrable property of Gaussian Hermitian model and $W_{1 + \infty}$ algebra in Fock representation. Motivated by this example, we propose a set of assumptions that may allow one to recover superintegrable polynomials. The main two assumptions are box adding/removing rule (Pierri rule) and existence of Hamiltonian for superintegrable polynomials. We detail our method in case of the Gaussian Hermitian model, and then apply it to the cubic Kontsevich model.
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Cited by 1 Pith paper
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Non-commutative creation operators for symmetric polynomials
Non-commutative creation operators B̂_m are built for symmetric polynomials in matrix and Fock representations of W_{1+∞} and affine Yangian algebras.
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