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Showing 1 to 3 of 3 for “"tau-functions"”.
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Connection Problem for Painlevé Tau Functions
… the differential identities for isomonodromic tau functions, describing their monodromy dependence. For Painlev´e equations we obtain them from the relation of tau function to classical action which is a consequence of quasihomogeneity of corresponding Hamiltonians. We use these identities to …
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Q-systems and generalizations in representation theory
We study tau-functions given as matrix elements for the action of loop groups, $\widehat{GL_n}$ on $n$-component fermionic Fock space. In the simplest case, $n=2$, the tau-functions are equal to Hankel determinants and applying the famous Desnanot-Jacobi identity, one can see that they satisfy a …
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Poisson structures and degenerations of integrable systems related to y (gl2)
… the variables in all these systems in terms of τ-functions, and use this to give the relation between the 2 × 2 and N × N Lax matrix descriptions of the systems. We show that all these systems are completely integrable, giving explicit action-angle variables. In the past, these three systems were …