Related papers: Irreducibility criterion for tensor products of Ya…
We study certain family of finite-dimensional modules over the Yangian $Y(gl_N)$. The algebra $Y(gl_N)$ comes equipped with a distinguished maximal commutative subalgebra $A(gl_n)$ generated by the centres of all algebras in the chain…
In this article, we study the representation theory of shifted super Yangians and finite $W$-superalgebras of type A. A criterion for the finite dimensionality of irreducible modules is obtained in the standard parity case. Furthermore, we…
In this paper, we investigate the irreducible tensor product modules over the planar Galilean conformal algebra $\mathcal{G}$ named by Aizawa, which is the infinite-dimensional Galilean conformal algebra introduced by Bagchi-Gopakumar in…
In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…
An action of the Yangian of the general Lie algebra gl(N) is defined on every irreducible integrable highest weight module of affine gl(N) with level greater than 1. This action is derived, by means of the Drinfeld duality and a subsequent…
We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…
We study the category O of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. Motivated by…
We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.
We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We…
In this paper, we study the representation theory of the universal central extension $\mathcal{G}$ of the infinite-dimensional Galilean conformal algebra, introduced by Bagchi-Gopakumar, in $(2+1)$ dimensional space-time, which was named…
We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of the linear group GL(n) representations and universal upper bounds on the relative dimensions of irreducible components of a tensor…
Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional…
We give explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra and of its twisted analogues, corresponding to symplectic and orthogonal Lie algebras. In particular, we develop the fusion…
We give an explicit criterion for the irreducibility of some induction products of evaluation modules of affine Hecke algebras of type A. This allows to describe the form of the singularities of the trigonometric R-matrix associated to any…
In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal…
We consider integrable category $\mathcal{O}$ representations of Borcherds--Kac--Moody algebras whose Cartan matrix is finite dimensional, and determine the necessary and sufficient conditions for which the tensor product of irreducible…
We are concerned with finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak osp}_{2n+1|2m}$. Every such representation is highest weight and we use embedding theorems…
Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…
We give several formulas for the character of an arbitrary irreducible finite--dimensional representation for the Yangian of sl_2.
In this paper, we consider the necessary and sufficient conditions for the tensor product of the fundamental representations for the restricted quantum loop algebras of type A at roots of unity to be irreducible.