Related papers: Locally free Caldero-Chapoton functions via reflec…

In a recent paper by K.-H. Lee and K. Lee, rigid reflections are defined for any Coxeter group via non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from an acyclic quiver, the rigid…

We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…

We present a series of algorithms for computing geometric and representation-theoretic invariants of Calogero-Moser spaces and rational Cherednik algebras associated to complex reflection groups. Especially, we are concerned with…

In this paper we showed that under two assumptions we are able to define interesting functions that we call generalized local coefficients. We showed that in the quasi-split case generalized local coefficients are up to a positive constant…

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE).…

We study skew-symmetrizable cluster algebras $\mathcal{A}$ associated with unpunctured surfaces $\tilde{\mathbf{S}}$ endowed with an orientation-preserving involution $\sigma$. We give a geometric realization of such cluster algebras by…

We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit expressions for Laurent expansions of the…

Let $\ell$ and $p$ be distinct primes, $n$ a positive integer, $F_\ell$ an $\ell$-adic local field of characteristic $0,$ and let $W(k)$ denote the ring of Witt vectors over an algebraically closed field of characteristic $p$. Work of…

We discuss the conical region of convergence of exponential and asymptotically polynomial form factors and their integral representations. Then, we calculate the spectral representation of the propagator of nonlocal theories with entire…

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of…

We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the "truncated simple reflections" on the set of almost…

We prove two compactness results for function spaces with finite Dirichlet energy of half-space nonlocal gradients. In each of these results, we provide sufficient conditions on a sequence of kernel functions that guarantee the asymptotic…

In the present paper 2-local derivations on various algebras of infinite dimensional matrix-valued functions on a compact are considered. It is proved that every 2-local derivation on such algebra is a derivation. Also we explain that the…

Inspired by recent work of Geiss-Leclerc-Schroer, we use Hom-finite cluster categories to give a good candidate set for a basis of (upper) cluster algebras with coefficients arising from quivers. This set consists of generic values taken by…

We study some properties of smoothing kernels and their local expression as they appear in the construction of Colombeau-type generalized function algebras which are diffeomorphism invariant.

Let $\mathrm{F}$ be a local non-archimedean field of residue characteristic $p$ and $\overline{\mathbb{F}}_\ell$ an algebraic closure of a finite field of characteristic $\ell \neq p$. We extend the results of Lapid and M\'inguez concerning…

Mapping a locally free module to its l-th tensor power gives rise to a natural map from the Grothendieck group of all locally free modules to the Grothendieck group of all locally free representations of the l-th symmetric group. In this…

Integral representations for continuous polynomial local functionals on convex functions are established in terms of a finite family of polynomials. This result is obtained by approximation from a classification of the dense subspace of…

We introduce and analyze the nonlocal variants of two Cahn-Hilliard type equations with reaction terms. The first one is the so-called Cahn-Hilliard-Oono equation which models, for instance, pattern formation in diblock-copolymers as well…

Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We…