Related papers: Linear recurrence relations in $Q$-systems and dif…
The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…
We use vertex operator algebras and intertwining operators to study certain substructures of standard $A_1^{(1)}$--modules, allowing us to conceptually obtain the classical Rogers--Ramanujan recursion. As a consequence we recover…
We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back…
We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…
We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. Corresponding to the recurrence relations with…
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
We derive decomposition formulas for supercharacters of quantum affine ortho-symplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type…
We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We present an ansatz of generalizing the construction of recursion relations for the correlation functions of the $\mathfrak{sl}_2$-invariant fundamental exchange model in the thermodynamic limit by Jimbo, Miwa, Smirnov, Takeyama and one of…
Using results from the theory of modular forms, we reprove and extend a result of Romik about lacunary recurrence relations for Eisenstein series.
We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that…
In this paper, we construct a linear positive operators q-parametric Szasz-Mirakjan operators generated by the q-Dunkl generalization of the exponential function. We obtain Korovkin's type approximation theorem for these operators and…
In this note we consider the algebra $U_q(\hat{sl}_\infty)$ and we study the category O of its integrable representations. The main motivations are applications to quantum toroidal algebras, more precisely predictions of character formulae…
Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…
We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary…
We study multiple recurrence properties along separated cross sections for pmp actions of unimodular lcsc group on Polish spaces. We establish a multiple transverse recurrence theorem under the assumption that sufficiently large powers of…
We use combinatorial description of bases of Feigin-Stoyanovsky's type subspaces of standard modules of level 1 for affine Lie algebras of types $A_\ell^{(1)}$ and $D_4^{(1)}$ to obtain character formulas. These descriptions naturally lead…
In this paper we obtained several properties that the characteristic polynomials of the unit-primitive matrix satisfy. In addition, using these properties we have shown that the recurrence relation given as in the formula (1) is true. In…
We derive some q-analogs of Euler-Cassini-type identities and of recurrence formulas for powers of Fibonacci polynomials.