Infinite Analysis Seminar Tokyo

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.)

2012/12/01

13:30-15:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Alexey Silantyev (Univ. Tokyo)
Manin matrices and quantum integrable systems (ENGLISH)
[ Abstract ]
Manin matrices (known also as right quantum matrices) is a class of
matrices with non-commutative entries. The natural generalization of the
usual determinant for these matrices is so-called column determinant.
Manin matrices, their determinants and minors have the most part of the
properties possessed by the usual number matrices. Manin matrices arise
from the RLL-relations and help to find quantum analogues of Poisson
commuting traces of powers of Lax operators and to establish relations
between different types of quantum commuting families. The RLL-relations
also give us q-analogues of Manin matrices in the case of trigonometric
R-matrix (which define commutation relations for the quantum affine
algebra).