Related papers: Braid Group Action on Affine Yangian
We define an action of the braid group of a simple Lie algebra on the space of imaginary roots in the corresponding quantum affine algebra. We then use this action to determine an explicit condition for a tensor product of arbitrary…
We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view…
The Drinfled realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization…
The faces of the braid arrangement form a monoid. The associated monoid algebra -- the face algebra -- is well-studied, especially in relation to card shuffling and other Markov chains. In this paper, we explore the action of the symmetric…
We define 2-functors on the categorified quantum group of a simply-laced Kac-Moody algebra that induce Lusztig's internal braid group action at the level of the Grothendieck group.
The Yangian of the Lie algebra $gl_N$ has a distinguished family of irreducible finite-dimensional representations, called elementary representations. They are parametrized by pairs, consisting of a skew Young diagram and a complex number.…
In the paper, we prove that there exists a braid group action on the extended crystal $\widehat{B}(\infty)$ of finite type. The extended crystal $\widehat{B}(\infty)$ and its braid group action are investigated from the viewpoint of crystal…
This is a review paper on the algebraic structure and representations of the A type Yangian and the B, C, D types twisted Yangians. Some applications to constructions of Casimir elements and characteristic identities for the corresponding…
We develop a theory of parabolic induction and restriction functors relating modules over Coulomb branch algebras, in the sense of Braverman-Finkelberg-Nakajima. Our functors generalize Bezrukavnikov-Etingof's induction and restriction…
We construct differential graded enhancements of the zigzag algebras which were used by Khovanov, Seidel and Thomas to produce categorical braid group actions. These enhancements are related to $p$-differential graded structures by a…
In this paper, we present a generalization of well-established results regarding symmetries of $\Bbbk$-algebras, where $\Bbbk$ is a field. Traditionally, for a $\Bbbk$-algebra $A$, the group $\Bbbk$-algebra automorphisms of $A$ captures the…
This paper gives a Schur-Weyl duality approach to the representation theory of the affine Hecke algebras of type C with unequal parameters. The first step is to realize the affine braid group of type $C_k$ as the group of braids on $k$…
This paper provides a unified approach to results on representations of affine Hecke algebras, cyclotomic Hecke algebras, affine BMW algebras, cyclotomic BMW algebras, Markov traces, Jacobi-Trudi type identities, dual pairs (Zelevinsky),…
This paper is devoted to the proof of a structural theorem, concerning certain homomorphic images of Artin braid group on $n$ strands in finite symmetric groups. It is shown that any one of these permutation groups is an extension of the…
We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalization of the Satake isomorphism for these algebras, relating it to integrable representations of the…
In this note, we consider the twisted Yangians $\text{Y}(\mathfrak{g}_N)$ associated with the orthogonal and symplectic Lie algebras $\mathfrak{g}_N=\mathfrak{o}_N,\mathfrak{sp}_N$. First, we introduce a certain subalgebra…
Let $\mathfrak{g}$ be a semisimple simply-laced Lie algebra of finite type. Let $\mathcal{C}$ be an abelian categorical representation of the quantum group $U_q(\mathfrak{g})$ categorifying an integrable representation $V$. The Artin braid…
This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence between geometric signatures and analytic representations is…
The problem of solving non-linear equations would be considerably simplified by a possibility to convert known solutions into the new ones. This could seem an element of art, but in the context of ADHM-like equations describing quiver…
We study the Yetter--Drinfeld D(B)-module algebra structure on the Heisenberg double H(B^*) endowed with a "heterotic" action of the Drinfeld double D(B). This action can be interpreted in the spirit of Lu's description of H(B^*) as a twist…