Instanton R-matrix and W-symmetry

Abstract

We study the relation between ${\mathcal{W}}_{1+\infty }$ algebra and Arbesfeld-Schiffmann-Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object linking these two pictures is the Miura transformation. Using the results of Nazarov and Sklyanin we find an explicit formula for the mixed R-matrix acting on two Fock spaces associated to two different asymptotic directions of the affine Yangian. Using the free field representation we propose an explicit identification of Arbesfeld-Schiffmann-Tsymbaliuk generators with the generators of Maulik-Okounkov Yangian. In the last part we use the Miura transformation to give a conformal field theoretic construction of conserved quantities and ladder operators in the quantum mechanical rational and trigonometric Calogero-Sutherland models on which a vector representation of the Yangian acts.

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Cited by in corpus (16)

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• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Liouville reflection operator, affine Yangian and Bethe ansatz
• Quantum toroidal algebras and solvable structures in gauge/string theory
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