dorsal/arxiv
View SchemaNon-Standard KP Evolution and Quantum $\tau$-function
| Authors | S. Kharchev, A. Mironov, A. Morozov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9501013 |
| URL | https://arxiv.org/abs/q-alg/9501013 |
| DOI | 10.1007/BF02066659 |
Abstract
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 {\it always} 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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"abstract": "One possible way to fix partly a ``canonical definition\u0027\u0027 of $\\tau$-functions\nbeyond the conventional KP/Toda framework could be to postulate that evolution\noperators are {\\it always} group elements. We discuss implications of this\npostulate for the first non-trivial case: fundamental representations of\nquantum groups $SL_q(N)$. It appears that the most suited (simple) for quantum\ndeformation framework is some non-standard formulation of KP/Toda systems. It\nturns out that the postulate needs to be slightly modified to take into account\nthat no ``nilpotent subgroups\u0027\u0027 exist in $SL_q(N)$ for $q\\neq 1$. This has some\ndefinite and simple implications for $q$-determinant-like representations of\nquantum $\\tau$-functions.",
"arxiv_id": "q-alg/9501013",
"authors": [
"S. Kharchev",
"A. Mironov",
"A. Morozov"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"doi": "10.1007/BF02066659",
"title": "Non-Standard KP Evolution and Quantum $\\tau$-function",
"url": "https://arxiv.org/abs/q-alg/9501013"
},
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