This is a review article on the quantum toroidal algebras, focusing on their roles in various
solvable structures of 2d conformal field theory, supersymmetric gauge theory, and string …

Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence
from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on …

A bstract We explore the quantum algebraic formalism of the gauge origami system in ℂ 4,
where D2/D4/D6/D8-branes are present. We demonstrate that the contour integral formulas …

A bstract We associate vertex operator algebras to (p, q)-webs of interfaces in the
topologically twisted\(\mathcal {N}= 4\) super Yang-Mills theory. Y-algebras associated to …

We study the relation between $\mathcal {W} _ {1+\infty} $ algebra and Arbesfeld-
Schiffmann-Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object …

A bstract Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY) and
shifted QY, were introduced, and they act on BPS states for non-compact toric Calabi-Yau …

A bstract We describe the general strategy for lifting the Wess-Zumino-Witten model from the
level of one-loop Kac-Moody\({U} _q {\left (\widehat {\mathfrak {g}}\right)} _k\) to generic …

We propose that Miura operators are R-matrices of certain infinite-dimensional quantum
algebras. We test our proposal by realizing Miura operators of $ q $-deformed $ W $-and $ Y …

A bstract We construct the elliptic Miura transformation and use it to obtain the expression of
the currents of elliptic corner VOA. We subsequently prove a novel combinatorial formula …

We consider the R-matrix of the quantum toroidal algebra of type gl 1, both abstractly and in
Fock space representations. We provide a survey of a certain point of view on this object …