Related papers: Yangian characters and classical W-algebras

By a generalized Yangian we mean a Yangian-like algebra of one of two classes. One of these classes consists of the so-called braided Yangians, introduced in our previous paper. The braided Yangians are in a sense similar to the reflection…

A $q$-analog of the Clebsch Gordan rules for the tensor products of the fundamental representations of Yangian is introduced. Its relation to the crystal base theory and application to the spinon character formulas are discussed in case of…

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra $\mathfrak{q}(n)$. It is given in terms of Brundan's work of finite-dimensional integer weight…

We use the isomorphisms between the $R$-matrix and Drinfeld presentations of the quantum affine algebras in types $B$, $C$ and $D$ produced in our previous work to describe finite-dimensional irreducible representations in the $R$-matrix…

Let $d$ be a positive integer. The Yangian $Y_d=Y(\mathfrak{gl}(d,\mathbb C))$ of the general linear Lie algebra $\mathfrak{gl}(d,\mathbb C)$ has countably many generators and quadratic-linear defining relations, which can be packed into a…

We study the truncated shifted Yangian $Y_{n,l}(\sigma)$ over an algebraically closed field $\mathbb{k}$ of characteristic $p > 0$, which is known to be isomorphic to the finite $W$-algebra $U(\mathfrak{g}, e)$ associated to a corresponding…

We generalize the positivity conjecture on (Kauffman bracket) skein algebras to Roger--Yang skein algebras. To generalize it, we use explicit polynomials like Chebyshev polynomials of the first kind to give candidates of positive bases.…

For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of Birman-Murakami-Wenzl type QM-algebras, we investigate a structure of its…

We construct a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(q_u-q_{u+1})$ to the universal enveloping algebra of a $W$-algebra associated with $\mathfrak{gl}(\sum_{s=1}^lq_s)$ and a nilpotent element of type…

We formulate a family of algebras, twisted Yangians (of simply-laced quasi-split type) in Drinfeld type current generators and defining relations. These new algebras admit PBW type bases and are shown to be a deformation of twisted current…

We consider boundary scattering for a semi-infinite one-dimensional deformed Hubbard chain with boundary conditions of the same type as for the Y=0 giant graviton in the AdS/CFT correspondence. We show that the recently constructed quantum…

Frenkel and Reshetikhin introduced q-characters to study finite dimensional representations of quantum affine algebras. In the simply laced case Nakajima defined deformations of q-characters called q,t-characters. The definition is…

We construct type $g\ell(n)$ Yangian algebra evaluations of order $N$ embedded in Heisenberg algebras and consider their representations having a highest weight. These Yangian algebra presentations depend on $nN$ parameters. We construct…

We raise the question of whether (a slightly generalized notion of) $qq$-characters can be constructed purely representation-theoretically. In the main example of the quantum toroidal $\mathfrak{gl}_1$ algebra, geometric engineering of…

Let g be a simple Lie algebra. We consider the category O-hat of those modules over the affine quantum group Uq(g-hat) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that…

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the…

We classify irreducible representations of finite $W$-algebra of the queer Lie superalgebra $Q(n)$ associated with the principal nilpotent coadjoint orbits. We use this classification and our previous results to obtain a classification of…

We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach by Guay-Nakajima-Wendlandt. We also prove that the quiver Yangians related by Seiberg duality are…

We give explicit formulas for the coproducts of modified Drinfeld-Cartan generating series for the Yangian in type $A$ and for the quantum affine algebras in the particular type $A_2$. As an auxiliary result of the latter, we give an…

Given a symmetric quiver with potential, we develop a geometric construction of shifted Yangians acting on the critical cohomologies of antidominantly framed quiver varieties with extended potentials, using the $R$-matrices constructed from…