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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 104, Number 1, Pages 129–143
(Mi tmf1329)
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This article is cited in 21 scientific papers (total in 21 papers)
Nonstandard KP evolution and the quantum $\tau$-function
S. M. Kharcheva, A. D. Mironovab, A. Yu. Morozovb a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
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 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.
Citation:
S. M. Kharchev, A. D. Mironov, A. Yu. Morozov, “Nonstandard KP evolution and the quantum $\tau$-function”, TMF, 104:1 (1995), 129–143; Theoret. and Math. Phys., 104:1 (1995), 866–878
Linking options:
https://www.mathnet.ru/eng/tmf1329 https://www.mathnet.ru/eng/tmf/v104/i1/p129
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Abstract page: | 356 | Full-text PDF : | 100 | References: | 47 | First page: | 2 |
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