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Email: mphys11@ipb.ac.rs

Abstracts
Takeo Kojima
Integrable Structure of deformed Walgebra $W_{q,t}({\mathfrak g})$, quadratic relations and integrals of motion
Deformed Walgebra $W_{q,t}({\mathfrak g})$ is an elliptic deformation (a twoparameter deformation) of the classical Walgebra ${\cal W}({\mathfrak g})$ in the KdV theory. We study integrable structure of deformed Walgebra $W_{q,t}({\mathfrak g})$. This talk is divided into Part I: quadratic relations and Part II: integrals of motion. In Part I, we obtain a closed set of quadratic relations of the W currents of the deformed W algebra $W_{q,t}({\mathfrak g})$. This allows us to define the deformed W algebra by generators and relations. We report the case ${\mathfrak g}=A(M,N)^{(1)}, A_{2N}^{(2)}$. In Part II, we study an elliptic deformation of the ${\mathfrak g}$KdV theory. We construct infinitely many commutative operators G_n that we call the nonlocal integrals of motion for $W_{q,t}({\mathfrak g})$. These operators G_n can be regarded as an elliptic deformation of the Hamiltonian of the ${\mathfrak g}$KdV theory. We report the case ${\mathfrak g}=D_N^{(1)}$. We start this talk with basic reviews on the W algebra in the conformal field theory, so that even beginners easily understand it without much prior knowledge. Part II is based on collaboration with Professor Michio Jimbo.


Organizer:
Institute of Physics Belgrade (University of Belgrade)
Belgrade, Serbia
Coorganizers:
Faculty of Mathematics
(University of Belgrade)
Belgrade, Serbia
Mathematical Institute
(Serbian Academy of Sciences and Arts)
Belgrade, Serbia
Serbian Academy of Nonlinear Sciences (SANS)
Belgrade, Serbia
ZOOM link for attending lectures online:
https://us06web.zoom.us/j/81395737972?pwd=kZEEjWagmat78h2FHLb4TMCsdM7ZF3.1
Meeting ID: 813 9573 7972
Passcode: 824870
