Related papers: Linear recurrence relations in $Q$-systems and dif…

The commutation relation $KL = LK$ between finite convolution integral operator $K$ and differential operator $L$ has implications for spectral properties of $K$. We characterize all operators $K$ admitting this commutation relation. Our…

For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…

We introduce an R-matrix formulation of qq-characters and corresponding Frenkel-Reshetikhin deformed W-algebras. The R-matrix featuring in the construction is of Ding-Iohara-Miki (DIM) algebra, while the type of the qq-character is…

The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation,…

We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations…

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…

Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…

We study properties of coefficients of a linear form, originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.

We explore the behaviour emerging from learning agents repeatedly interacting strategically for a wide range of learning dynamics, including $Q$-learning, projected gradient, replicator and log-barrier dynamics. Going beyond the better…

We establish three-term recurrence relations for the ${}_1\phi_1$ and ${}_0\phi_1$ basic hypergeometric series involving multiplicative shifts of the parameters and the variable by integer powers of q. The coefficients of these recurrence…

For a quantum affine algebra of type A, we describe the composition series of the tensor product of a general minimal affinization with a Kirillov-Resehtikhin module associated to an extreme node of the Dynkin diagram of the underlying…

We obtain new explicit formulas for the recurrence coefficients of the q-orthogonal polynomial sequences in a class that extends the q-Askey scheme. Our formulas express the recurrence coefficients in terms of four parameters that determine…

We study a category O of representations of the Yangian associated to an arbitrary finite-dimensional complex simple Lie algebra. We obtain asymptotic modules as analytic continuation of a family of finite-dimensional modules, the…

Foundational material on complex Lie supergroups and their radial operators is presented. In particular, Berezin's recursion formula for describing the radial parts of fundamental operators in general linear and ortho-symplectic cases is…

The universal character is a polynomial attached to a pair of partitions and is a generalization of the Schur polynomial. In this paper, we introduce an integrable system of q-difference lattice equations satisfied by the universal…

We prove the Kuniba-Nakanishi-Suzuki (KNS) conjecture concerning the quantum dimension solution of the $Q$-system of type $D_r$ obtained by a certain specialization of classical characters of the Kirillov-Reshetikhin modules. To this end,…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…

Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…

In this paper we give a direct proof of the equality of certain generating function associated with tensor product multiplicities of Kirillov-Reshetikhin modules for each simple Lie algebra g. Together with the theorems of Nakajima and…