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- W1630550174 abstract "This paper is a brief review of recent results on the concept of ``generalized $tau$-function'', defined as a generating function of all the matrix elements in a given highest-weight representation of a universal enveloping algebra ${cal G}$. Despite the differences from the particular case of conventional $tau$-functions of integrable (KP and Toda lattice) hierarchies, these generic $tau$-functions also satisfy bilinear Hirota-like equations, which can be deduced from manipulations with intertwining operators. The main example considered in details is the case of quantum groups, when such $tau$-``functions'' are not $c$-numbers but take their values in non-commutative algebras (of functions on the quantum group $G$). The paper contains only illustrative calculations for the simplest case of the algebra SL(2) and its quantum counterpart $SL_q(2)$, as well as for the system of fundamental representations of SL(n)." @default.
- W1630550174 created "2016-06-24" @default.
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- W1630550174 date "1994-09-29" @default.
- W1630550174 modified "2023-10-16" @default.
- W1630550174 title "Quantum Deformations of $tau$-functions, Bilinear Identities and Representation Theory" @default.
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- W1630550174 doi "https://doi.org/10.48550/arxiv.hep-th/9409190" @default.
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