Related papers: Multiplicities and tensor product coefficients for…

In this paper, we investigate a connection between convolution products for quiver Hecke algebras and tensor products for quantum groups. We give a categorification of the natural projection $ \pi_{\lambda, \mu} :…

We establish the characterizations of commutators of several versions of maximal functions on spaces of homogeneous type. In addition, with the aid of interpolation theory, we provide weighted version of the commutator theorems by…

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…

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with…

We propose an $r$-variable version of Kostka-Shoji polynomials $K^-_{\lambda\mu}$ for $r$-multipartitions $\lambda,\mu$. Our version has positive integral coefficients and encodes the graded multiplicities in the space of global sections of…

The aim of this paper is to study the multipliers from $A_{r}(I)$ to $A_{p}(I), r \ne p$, where $I=(0,\infty)$ is the locally compact topological semigroup with multiplication max and usual topology and $A_{r}(I) = \{f \in L_{1}(I)\hbox{:}…

Let $\mathfrak{g}$ be a reductive Lie algebra and let $\vec{V}(\vec{\lambda})$ be a tensor product of $k$ copies of finite dimensional irreducible $\mathfrak{g}$-modules. Choosing $k$ points in $\mathbb{C}$, $\vec{V}(\vec{\lambda})$…

Let $A$ be the locally unital algebra associated to a cyclotomic oriented Brauer category over an arbitrary algebraically closed field $\Bbbk$ of characteristic $p\ge 0$. The category of locally finite dimensional representations of $A $ is…

Let $r \geq 0$, and let $\lambda$ and $\mu$ be partitions such that $\lambda_1 \leq r + 1$. We present a combinatorial interpretation of the plethysm coefficient $\langle s_\lambda, s_\mu[s_r] \rangle$. As a consequence, we solve the…

This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…

We introduce the new combinatorial approach of plethystic type of tableaux, as a method to understand coefficients of Schur functions appearing in plethysms $s_\nu[h_\lambda]$ and $s_{\nu}[e_{\lambda}]$, for any partitions $\lambda$ and…

Quantum topological invariants have played an important role in computational topology, and they are at the heart of major modern mathematical conjectures. In this article, we study the experimental problem of computing large $r$ values of…

Let $J_r$ denote an $r\times r$ matrix over a finite field $F$ with minimal and characteristic polynomials $(t-1)^r$. Suppose $r\leq s$. It is not hard to show that the Jordan canonical form of $J_r\otimes J_s$ is similar to…

We prove a H\"{o}rmander type multiplier theorem for multilinear Fourier multipiers with multiple weights. We also give weighted estimates for their commutators with vector $BMO$ functions.

We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…

For $G$ a complex reductive group and $B \subseteq G$ a Borel subgroup, we provide a reduction rule for certain weight multiplicities in Demazure modules $V_\lambda^w$: given a weight $\mu$ on a face of the associated weight polytope…

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…

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and…

In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the…