The Integrals of Motion for the Deformed W-Algebra $W_{qt}(sl_N^)$ II: Proof of the commutation relations

Details The Integrals of Motion for the Deformed W-Algebra $W_{qt}(sl_N^)$ II: Proof of the commutation relations The Integrals of Motion for the Deformed W-Algebra $W_{qt}(sl_N^)$ II: Proof of the commutation relations

2007-09-14

arxiv.org/abs/0709.2305v1

Physics

Mathematical Physics

Dedicated to Professor Tetsuji Miwa on the occasion on the 60th birthday

Scientific paper

10.1007/s00220-008-0524-3

We explicitly construct two classes of infinitly many commutative operators
in terms of the deformed W-algebra $W_{qt}(sl_N^)$, and give proofs of the
commutation relations of these operators. We call one of them local integrals
of motion and the other nonlocal one, since they can be regarded as elliptic
deformation of local and nonlocal integrals of motion for the $W_N$ algebra.

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