RTT presentation of finite W-algebras

Abstract

We construct a wide class of finite W-algebras as truncations of Yangians. These truncations correspond to algebra homomorphisms and allow to construct the W-algebras as exchange algebras, the R-matrix being the Yangian's one. As an application, we classify all irreducible finite dimensionnal representations of these W-algebras and determine their center.

31 pages Part on representations corrected and completed; misprints corrected

References in corpus (5)

• Finite-dimensional irreducible representations of twisted Yangians
• Yangian realisations from finite W algebras
• Yangian symmetry in the Non Linear Schrodinger hierarchy
• Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy
• Deformed W_N algebras from elliptic sl(N) algebras

Cited by in corpus (11)

• Parabolic presentations of the Yangian Y(gl_n)
• Representations of reflection algebras
• Explicit generators in rectangular affine W-algebras of type A
• Twisted Yangians and folded W-algebras
• The $R$-matrix presentation for the Yangian of a simple Lie algebra
• W-superalgebras as truncation of super-Yangians
• Finite W-superalgebras and truncated super Yangians
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• R-matrix realization of two-parameter quantum group U_{r,s}(gl_n)
• Principal Realization of the Yangian Y(gl(n))
• A Drinfeld type presentation of twisted Yangians