Affine super Yangians and rectangular <i>W</i>-superalgebras
Mamoru Ueda
Abstract
Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from the affine super Yangian Yε1,ε2(sl̂(m|n)) to the universal enveloping algebra of the rectangular W-superalgebra Wk(gl(ml|nl),(l(m|n))) for all m ≠ n, m, n ≥ 2 or m ≥ 3, n = 0. Furthermore, we show that the image of this homomorphism is dense, provided that k + (m − n)(l − 1) ≠ 0.
Topics & Concepts
YangianHomomorphismAffine transformationMathematicsConjectureLie superalgebraSuperalgebraPure mathematicsAlgebra homomorphismCombinatoricsImage (mathematics)Algebra over a fieldQuantum affine algebraCurrent algebraCellular algebraAlgebra representationAffine Lie algebraComputer scienceArtificial intelligenceAlgebraic structures and combinatorial modelsAdvanced Topics in AlgebraNonlinear Waves and Solitons