相关论文: Non symmetric Cauchy kernels for the classical Gro…

We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal…

We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly"…

In this paper, we show that the kernel function of Cauchy type for type $BC$ intertwines the commuting family of van Diejen's $q$-difference operators. This result gives rise to a transformation formula for certain multiple basic…

We consider random walk polynomial sequences $(P_n(x))_{n\in\mathbb{N}_0}\subseteq\mathbb{R}[x]$ given by recurrence relations of the form $P_0(x)=1$, $P_1(x)=x$ and $x P_n(x)=a_n P_{n+1}(x)+c_n P_{n-1}(x)\;(n\in\mathbb{N})$, where $a_n$…

We prove a restriction of an analogue of the Robinson--Schensted--Knuth correspondence for semi-skyline augmented fillings, due to Mason, to multisets of cells of a staircase possibly truncated by a smaller staircase at the upper left end…

We give an easy diagrammatical description of the parabolic Kazhdan-Lusztig polynomials for the Weyl group $W_n$ of type $D_n$ with parabolic subgroup of type $A_n$ and consequently an explicit counting formula for the dimension of the…

We consider a new class of matrices associated to a real square matrix $A$ and to a vector $\vec{c} \in \{-1,1\}^n$ such that $c_1=1$ by using a map $\varphi_{\vec{c}}$ which turns out to be a conjugation of a matrix $A$ by a signature…

Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials.…

We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both…

We consider a multivariate version of the so-called Lancaster problem of characterizing canonical correlation coefficients of symmetric bivariate distributions with identical marginals and orthogonal polynomial expansions. The marginal…

We introduce an analogue $K_n(x,z;q,t)$ of the Cauchy-type kernel function for the Macdonald polynomials, being constructed in the tensor product of the ring of symmetric functions and the commutative algebra $\mathcal{A}$ over the…

We investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition there corresponds a quantum symmetry which is the identity when applied twice. As an application,…

We express cluster variables of type $B_n$ and $C_n$ in terms of cluster variables of type $A_n$. Then we associate a cluster tilted bound symmetric quiver $Q$ of type $A_{2n-1}$ to any seed of a cluster algebra of type $B_n$ and $C_n$.…

The kernel of the natural projection of a graph product of groups onto their direct product is called the Cartesian subgroup of the graph product. This construction generalises commutator subgroups of right-angled Coxeter and Artin groups.…

New criteria for which Cayley graphs of cyclic groups of any order can be completely determined--up to isomorphism--by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley…

We consider the sample covariance matrices of large data matrices which have i.i.d. complex matrix entries and which are non-square in the sense that the difference between the number of rows and the number of columns tends to infinity. We…

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a…

This work explores classical discrete multiple orthogonal polynomials, including Hahn, Meixner of the first and second kinds, Kravchuk, and Charlier polynomials, with an arbitrary number of weights. Explicit expressions for the recursion…

Using the formalism of quantizers and dequantizers, we show that the characters of irreducible unitary representations of finite and compact groups provide kernels for star products of complex-valued functions of the group elements.…

In a digraph, a kernel is a subset of vertices that is both independent and absorbing. Kernels have important applications in combinatorics and outside. Kernels do not always exist and finding sufficient conditions ensuring their existence…