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arxiv nlin/0305001 v2 pith:NFMMMZJ7 submitted 2003-04-30 nlin.SI

Hypergeometric tau functions τ({bf t},T,{bf t}^*) as infty-soliton tau function in T variables

classification nlin.SI
keywords functiondualhierarchyhypergeometricparameterssolitonsolutionvariables
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We consider KP tau function of hypergeometric type $\tau({\bf t},T,{\bf t}^*)$, where the set ${\bf t}$ is the KP higher times and $T,{\bf t}^*$ are sets of parameters. Fixing ${\bf t}^*$, we find that $\tau({\bf t},T,{\bf t}^*)$ is an infinite-soliton solution of different (dual) multi-component KP (and TL) hierarchy, where the roles of the variables ${\bf t}$ and $T$ are interchanged. When $\tau({\bf t},T,{\bf t}^*)$ is a polynomial in ${\bf t}$, we obtain a $N$-soliton solution of the dual hierarchy. Parameters of the solitons are related to the Frobenius coordinates of partitions in the Schur function development of $\tau({\bf t},T,{\bf t}^*)$.

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  1. Superintegrability for some $(q,t)$-deformed matrix models

    hep-th 2025-10 unverdicted novelty 7.0

    Proves uniqueness of solutions to constraints on (q,t)-deformed hypergeometric functions and derives superintegrability relations for a general (q,t)-deformed matrix model with allowed parameters.