English

Instanton R-matrix and W-symmetry

High Energy Physics - Theory 2020-01-29 v1 Mathematical Physics math.MP Quantum Algebra

Abstract

We study the relation between W1+\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.

Cite

@article{arxiv.1903.10372,
  title  = {Instanton R-matrix and W-symmetry},
  author = {Tomáš Procházka},
  journal= {arXiv preprint arXiv:1903.10372},
  year   = {2020}
}

Comments

no figures

R2 v1 2026-06-23T08:18:18.589Z