Related papers: Yangians: their Representations and Characters

The character formula of any finite dimensional irreducible module $L_\lambda$ for Lie superalgebra $\mathfrak{osp}(n|2)$ is computed. As a by-product, the decomposition of tensor module $L_\lambda\otimes \mathbb{C}^{n|2}$, where…

In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.

The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak q(n)$ over $\C$ was solved in 1996 by I. Penkov and V. Serganova. In this article, we give a different approach…

This article gives a summary of the finite-dimesional irreducible representations of the $q$-Onsager algebra, which are treated in detail in our paper `The augmented tridiagonal algebra'.

Because of its multiplicativity, the Berezinian is the character of the one-dimensional representation of the general linear supergroup. We give an explicit construction of this representation on a space of tensors. Similarly, we construct…

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations…

We give a new proof of the fact that the super Yangian of general linear Lie superalgebra is isomorphic to the finite W-superalgebra of the general linear Lie superalgebra associated to a rectangular nilpotent element.

We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the…

We classify the finite-dimensional irreducible linear representations of the Baumslag-Solitar groups BS(p,q) = < a, b | a b^p = b^q a > for relatively prime p and q. The general strategy of the argument is to consider the matrix group given…

Let $\mathbb{F}_{q}$ be a finite field of characteristic $p$ and let $W_{2}(\mathbb{F}_{q})$ be the ring of Witt vectors of length two over $\mathbb{F}_{q}$. We prove that for any integer $n$ such that $p$ divides $n$, the groups…

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.

Let g be the Lie superalgebra p(3) of rank 2 over an algebraically closed field K of characteristic p > 3. We classify all irreducible modules of g, and give the character formulae for irreducible modules.

All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.

We present a construction of all finite indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level at most 2 with abelian permutation group. As a consequence, we obtain a formula for the number of such…

We recall the classification of the irreducible representations of $SL(2)_q$, and then give fusion rules for these representations. We also consider the problem of $\cR$-matrices, intertwiners of the differently ordered tensor products of…

We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…

We classify all conformal irreducible modules of finite type over the Cheng Kac superalgebra CK(6).

The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding…

We derive closed formulae for the first examples of non-algebraic, elliptic `leading singularities' in planar, maximally supersymmetric Yang-Mills theory and show that they are Yangian-invariant.