Yangian realisations from finite W algebras

Abstract

We construct an algebra homomorphism between the Yangian Y(sl(n)) and the finite W-algebras W(sl(np),n.sl(p)) for any p. We show how this result can be applied to determine properties of the finite dimensional representations of such W-algebras.

26 pages, Latex2e

Cited by in corpus (27)

• Finite vs. affine W-algebras
• W-symmetry, topological vertex and affine Yangian
• Cohomological Hall algebras, vertex algebras and instantons
• Representations of reflection algebras
• Nonlinear holomorphic supersymmetry, Dolan-Grady relations and Onsager algebra
• Explicit generators in rectangular affine W-algebras of type A
• Affine Super Yangians and Rectangular $W$-superalgebras
• Twisted Yangians and folded W-algebras
• W-superalgebras as truncation of super-Yangians
• Principal Galois orders and Gelfand-Zeitlin modules
• The $R$-matrix presentation for the Yangian of a simple Lie algebra
• Nonlinear Holomorphic Supersymmetry on Riemann Surfaces
• Finite W-superalgebras via super Yangians
• Finite W-superalgebras and truncated super Yangians
• On shifted super Yangians and a class of finite W-superalgebras
• Parabolic presentations of the super Yangian $Y({\mathfrak{gl}}_{M|N})$ associated with arbitrary 01-sequences
• RTT presentation of finite W-algebras
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• On the finite $W$-algebra for the Lie superalgebra Q(N) in the non-regular case
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra
• Finite W-algebras for gl_N
• The Higher Spin Rectangle
• Dirac reductions and Classical W-algebras
• Proof of 5D $A_n$ AGT conjecture at $\beta =1$
• Generalized finite and affine $W$-algebras in type $A$
• Deformed oscillators algebra formulation of the Nonlinear Schrodinger hierarchy and of its symmetry