Related papers: Weight-dependent commutation relations and combina…
To any Hamiltonian action of a reductive algebraic group $G$ on a smooth irreducible symplectic variety $X$ we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. For cotangent bundles our…
The model of generalized quons is described in a purely algebraic way. Commutation relations and corresponding consistency conditions for our generalized quons system are studied in terms of quantum Weyl algebras. Fock space representation…
Generalized Baxter's TQ-relations and the QQ-system are systems of algebraic relations in the category O of representations of the Borel subalgebra of the quantum affine algebra U_q(g^), which we established in our earlier works…
In combinatorial representation theory, Kostant's weight multiplicity formula $m(\lambda,\mu)$ is a tool that provides a means of determining the multiplicity of a weight $\mu$ in the adjoint representation of a simple Lie algebra…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components…
We study root systems equipped with a basis of dominant weights such that certain axioms hold. This formalism allows to define a linear basis P of the space of Weyl group invariant polynomials. This basis is actually a family depending on…
In this work we characterize the combinatorial metrics admitting a MacWilliams-type identity and describe the group of linear isometries of such metrics. Considering coverings that are not connected, we classify the metrics satisfying the…
Weight systems are functions on chord diagrams satisfying Vassiliev's $4$-term relations. They originate in the theory of finite type knot invariants. Recent developments in understanding weight systems arising from Lie algebras are based…
Given a weighted $\ell^2$ space with weights associated to an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a…
We consider elliptic transmission problems with complex coefficients across an interface. Under proper transmission conditions, that extend known conditions for well-posedness, and sub-ellipticity we derive microlocal and local Carleman…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
We study the generalized rank weight distribution of a linear code. First, we provide a MacWilliams-type identity which relates the distributions of a code and its dual. Then, we give a formula for the enumerator polynomial. Finally, we…
We derive in detail four important results on integrals of Bessel functions from which three combinatorial identities are extracted. We present the probabilistic interpretation of these identities in terms of different types of random…
In this paper, we derive basic identities of symmetry in two variables related to higher-order q-Euler polynomials and q-analogue of higher order alternating power sums. The derivation of identities are based on the multibvariate p-adic…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.…
Motivated by recent interests in predictive inference under distribution shift, we study the problem of approximating finite weighted exchangeable sequences by a mixture of finite sequences with independent terms. Various bounds are derived…
We obtain several determinant evaluations, related to affine root systems, which provide elliptic extensions of Weyl denominator formulas. Some of these are new, also in the polynomial special case, while others yield new proofs of the…