Related papers: Braid Group Action on Affine Yangian

The theory of Nichols algebras of diagonal type is known to be closely related to that of semisimple Lie algebras. In this paper the connection between both theories is made closer. For any Nichols algebra of diagonal type invertible…

Enhanced gauge symmetry appears in Type II string theory (as well as F- and M-theory) compactified on Calabi--Yau manifolds containing exceptional divisors meeting in Dynkin configurations. It is shown that in many such cases, at enhanced…

Let g be a symmetrisable Kac-Moody algebra and U_h(g) its quantised enveloping algebra. Answering a question of P. Etingof, we prove that the quantum Weyl group operators of U_h(g) give rise to a canonical action of the pure braid group of…

Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution $(X,r)$ consists of a set $X$ and a bijective map $r:X\times X\to X\times X$ which satisfies the…

The group described in this paper appeared while studying fundamental groups of complements of branch curves. It turned out that a certain quotient of the braid group acts on those fundamental groups and studying this action is essential…

A general scheme of construction of Drinfeldians and Yangians from quantum non-twisted affine Kac-Moody algebras is presented. Explicit description of Drinfeldians and Yangians for all Lie algebras of the classical series A, B, C, D are…

The connection between simple Lie algebras and their Yangian algebras has a long history. In this work, we construct finite-dimensional representations of Yangian algebras $\mathsf{Y}(\mathfrak{sl}_{n})$ using the quiver approach. Starting…

We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie…

We define an action of the extended affine d-strand braid group on the open positroid stratum in the Grassmannian Gr(k,n), for d the greatest common divisor of k and n. The action is by quasi-automorphisms of the cluster structure on the…

We compute the braided groups and braided matrices $B(R)$ for the solution $R$ of the Yang-Baxter equation associated to the quantum Heisenberg group. We also show that a particular extension of the quantum Heisenberg group is dual to the…

We establish a degeneration isomorphism between quantum toroidal algebras and untwisted affine Yangians, valid for all untwisted affine Kac-Moody Lie algebras. Specifically, we prove that the affine Yangian $Y_\hbar(\mathfrak{g})$ is…

We study a certain discrete differentiation of piecewise-constant functions on the adjoint of the braid hyperplane arrangement, defined by taking finite-differences across hyperplanes. In terms of Aguiar-Mahajan's Lie theory of hyperplane…

We construct a unique braid group action on modified $q$-Weyl algebra $\mathbf A_q(S)$. Under this action, we give a realization of the braid group action on quasi-split $\imath$quantum groups $^{\imath}\mathbf U(S)$ of type…

In this paper we study a quadratic Poisson algebra structure on the space of bilinear forms on $C^{N}$ with the property that for any $n,m\in N$ such that $n m =N$, the restriction of the Poisson algebra to the space of bilinear forms with…

We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action allows us to see the algebra as the regular algebra in the…

We investigate deformations of skew group algebras arising from the action of the symmetric group on polynomial rings over fields of arbitrary characteristic. Over the real or complex numbers, Lusztig's graded affine Hecke algebra and…

We show that the braided Hochschild cohomology, of an algebra in a suitably algebraic braided monoidal category, admits a graded ring structure under which it is braided commutative. We then give a canonical identification between the usual…

We consider the quiver Yangians associated to general affine Dynkin diagrams. Although the quivers are generically not toric, the algebras have some similar structures. The odd reflections of the affine Dynkin diagrams should correspond to…

Starting from the free field realization of Kac-Moody Lie algebra, we define a generalized Yang-Yang function. Then for the Lie algebra of type $A_{n}$, we derive braiding and fusion matrix by braiding the thimble from the generalized…

We construct a braided analogue of the quantum permutation group and show that it is the universal braided compact quantum group acting on a finite space in the category of $\mathbb{Z}/N\mathbb{Z}$-$\textrm{C}^*$-algebras with a twisted…