## 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

### 2008年06月14日(土)

13:30-16:00   数理科学研究科棟(駒場) 117号室

Confluent KZ equations for $sl_2$ and quantization of monodromy preserving deformation
[ 講演概要 ]
We obtain a system of confluent Knizhnik-Zamolodchikov (KZ) equations which generalizes that of KZ equations for $sl_2$,
and give integral solutions of the system. We also study the relation between the system and monodromy preserving deformation theory,
and recover quantizations of Painlev\\'e equations P_I-P_V with affine Weyl group symmetry which are introduced by H.Nagoya.
Paul A. Pearce 氏 (Univ. of Melbourne) 15:00-16:00
Exact Solution and Physical Combinatorics of Critical Dense
Polymers
[ 講演概要 ]
A Yang-Baxter integrable model of critical dense polymers on the
square lattice
is introduced corresponding to the first member ${\\cal LM}(1,2)$ of a
family of logarithmic
minimal models. The model has no local degrees of freedom, only non-
local degrees
of freedom in the form of extended polymers. The model is built
diagrammatically using the
planar Temperley-Lieb algebra and solved exactly on finite width
strips using transfer matrix
techniques. The bulk and boundary free energies and finite-size
corrections are
obtained from the Euler-Maclaurin formula. The spectra are classified
by selection rules and
the physical combinatorics of the eigenvalue patterns of zeros in the
complex
spectral-parameter plane. This yields explicit finitized conformal
characters.
In particular, in the scaling limit, we confirm the central charge
$c=-2$ and conformal weights
$\\Delta_{1,s}=\\frac{(2-s)^2-1}{8}$ for $s=1,2,3,\\ldots$ where $s-1$ is
the number
of defects.