Toward a Canonical Qkdv Equation
نویسنده
چکیده
In [2, 3] we gave a number of formulas for qKdV equations derived in a q-Virasoro context. The constructions were meaningful even though the cocycle terms did not visibly satisfy a Jacobi identity. In the present note we modify the framework slightly and produce a cocycle term (morally equivalent to one of those used in [2, 3]) and thereby exhibit a more convincing candidate for a canonical qKdV equation. It remains to see how this is connected to the qKdV equation from the hierarchy picture. For background on q-analysis etc. we refer to [4].
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Aspects of Quantum Groups and Integrable Systems
Many q-differential operators arise in the study of q-special functions, Casimir operators, quantum groups, and representation theory. There are also natural origins via quantum integrable systems and the quantization of classical integrable systems. The latter is often expressed via a q-hierarchy picture akin to the standard Hirota–Lax–Sato formulation and this has many canonical aspects. On t...
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