## 東京無限可積分系セミナー

開催情報 土曜日　13:30～16:00　数理科学研究科棟(駒場) 117号室 神保道夫、国場敦夫、山田裕二、武部尚志、高木太一郎、白石潤一 https://www.ms.u-tokyo.ac.jp/~takebe/iat/index-j.html

### 2012年12月01日(土)

13:30-15:00   数理科学研究科棟(駒場) 117号室
アレクセイ　シランティエフ 氏 (東大数理)
Manin matrices and quantum integrable systems (ENGLISH)
[ 講演概要 ]
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).