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Communications in Mathematical Physics

, Volume 283, Issue 3, pp 795–851 | Cite as

The Integrals of Motion for the Deformed W-Algebra \({W_{q,t}(\widehat{gl_N})}\). II. Proof of the Commutation Relations

  • Takeo KojimaEmail author
  • Jun’ichi Shiraishi
Article

Abstract

We explicitly construct two classes of infinitely many commutative operators in terms of the deformed W-algebra \({W_{q,t}(\widehat{gl_N})}\), and give proofs of the commutation relations of these operators. We call one of them local integrals of motion and the other nonlocal, since they can be regarded as elliptic deformations of local and nonlocal integrals of motion for the Virasoro algebra and the W 3 algebra [1,2].

Keywords

Commutation Relation Analytic Continuation Integral Contour Weak Sense Monodromy Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematics, College of Science and TechnologyNihon UniversityTokyoJapan
  2. 2.Graduate School of Mathematical ScienceUniversity of TokyoTokyoJapan

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