Soliton theory, symmetric functions and matrix integrals. (English) Zbl 1146.37355
Summary: We consider a certain scalar product of symmetric functions which is parameterized by a function \(r\) and an integer \(n\). On the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of this product with the help of multi-integrals. This gives links between a theory of symmetric functions, soliton theory and models of random matrices (such as a model of normal matrices).
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 05E05 | Symmetric functions and generalizations |
| 33C70 | Other hypergeometric functions and integrals in several variables |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 60A10 | Probabilistic measure theory |
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