Related papers: Vector partition function and representation theor…

We use induction from parabolic subalgebras with infinite-dimensional Levi factor to construct new families of irreducible representations for arbitrary Affine Kac-Moody algebra. Our first construction defines a functor from the category of…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

We use Gelfand-Tsetlin diagrams to write down the weight multiplicity function for the Lie algebra sl_k(C) (type A_{k-1}) as a single partition function. This allows us to apply known results about partition functions to derive interesting…

A certain representation for the Heisenberg algebra in finite-difference operators is established. The Lie-algebraic procedure of discretization of differential equations with isospectral property is proposed. Using $sl_2$-algebra based…

We consider a tensor product $V(b)= \otimes_{i=1}^n\C^N(b_i)$ of the Yangian $Y(gl_N)$ evaluation vector representations. We consider the action of the commutative Bethe subalgebra $B^q \subset Y(gl_N)$ on a $gl_N$-weight subspace…

We introduce an algorithm to decompose orthogonal matrix representations of the symmetric group over the reals into irreducible representations, which as a by-product also computes the multiplicities of the irreducible representations. The…

We develop a theory of Jacobi polynomials for parabolic subgroups of finite reflection groups that specializes to the cases studied by Heckman and Opdam in which the whole group and the trivial group are considered. For the intermediate…

For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

In most applications of semi-simple Lie groups and algebras representation theory, calculating weight multiplicities is one of the most often used and effort consuming operations. The existing tools were created many years ago by Kostant…

Certain computable polynomials are described whose leading coefficients are equal to multiplicities in the tensor product decomposition for representations of a Lie algebra of ADE type.

Using the $\mathbb{R}((X))$-measure, we define and study certain $\mathbb{C}((X))$-valued functions on $\mathrm{GL}_n(F)$ for $F$ a two-dimensional local field. In particular, we define a convolution product on such suitable functions,…

For a set of nonnegative integers $S$ let $R_{S}(n)$ denote the number of unordered representations of the integer $n$ as the sum of two different terms from $S$. In this paper we focus on partitions of the natural numbers into two sets…

The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…

We construct irreducible representations of affine Khovanov-Lauda-Rouquier algebras of arbitrary finite type. The irreducible representations arise as simple heads of appropriate induced modules, and thus our construction is similar to that…

We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and…

Let $\mathfrak{d}$ be the Lie superalgebra of superderivations of the sheaf of sections of the exterior algebra of the homogeneous vector bundle $E$ over the flag variety $G/P$, where $G$ is a simple finite-dimensional complex Lie group and…

In this paper we establish a connection between the associated variety of a representation and the existence of certain degenerate Whittaker functionals, for both smooth and K-finite vectors, for all quasi-split real reductive groups,…

We construct and study in detail various dual pairs acting on some Fock representations between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit…

A conjecture of Kac states that the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field with given dimension vector has positive coefficients and furthermore that its constant term is…