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- W2083974311 abstract "We introduce and study ?isomonodromy? transformations of the matrix linear difference equation Y (z + 1) = A(z)Y (z) with polynomial A(z). Our main result is construction of an isomonodromy action of Zm(n+1)-1 on the space of coefficients A(z) (here m is the size of matrices and n is the degree of A(z)). The (birational) action of certain rank n subgroups can be described by difference analogs of the classical Schlesinger equations, and we prove that for generic initial conditions these difference Schlesinger equations have a unique solution. We also show that both the classical Schlesinger equations and the Schlesinger transformations known in isomonodromy theory, can be obtained as limits of our action in two different limit regimes. Similarly to the continuous case, for m = n = 2 the difference Schlesinger equations and their q-analogs yield discrete Painlev?e equations; examples include dPII, dPIV, dPV, and q-PVI." @default.
- W2083974311 created "2016-06-24" @default.
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- W2083974311 date "2004-11-01" @default.
- W2083974311 modified "2023-09-27" @default.
- W2083974311 title "Isomonodromy transformations of linear systems of difference equations" @default.
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- W2083974311 doi "https://doi.org/10.4007/annals.2004.160.1141" @default.
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