Geodesic
Nonstandard KP evolution and the quantum $\tau$-function
Teoretičeskaâ i matematičeskaâ fizika, Tome 104 (1995) no. 1, pp. 129-143

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One possible way to fix partly a “canonical definition” of $\tau$-functions beyond the conventional KP/Toda framework could be to postulate that evolution operators are group elements. We discuss implications of this postulate for the first non-trivial case: fundamental representations of quantum groups $SL_q(N)$. It appears that the most suited (simple) for quantum deformation framework is some non-standard formulation of KP/Toda systems. It turns out that the postulate needs to be slightly modified to take into account that no “nilpotent subgroups” exist in $SL_q(N)$ for $q\neq 1$. This has some definite and simple implications for $q$-determinant-like representations of quantum $\tau$-functions. 
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     author = {S. M. Kharchev and A. D. Mironov and A. Yu. Morozov},
     title = {Nonstandard {KP} evolution and the quantum $\tau$-function},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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S. M. Kharchev; A. D. Mironov; A. Yu. Morozov. Nonstandard KP evolution and the quantum $\tau$-function. Teoretičeskaâ i matematičeskaâ fizika, Tome 104 (1995) no. 1, pp. 129-143. http://geodesic.mathdoc.fr/item/TMF_1995_104_1_a9/