Related papers: Harder-Narasimhan Filtrations of Persistence Modul…
We prove that the weight multiplicities of the integrable irreducible highest weight module over the Kac-Moody algebra associated to a quiver are equal to the root multiplicities of the Kac-Moody algebra associated to some enlarged quiver.…
Naisse and Vaz defined an extension of KLR algebras to categorify Verma modules. We realise these algebras geometrically as convolution algebras in Borel-Moore homology. For this we introduce Grassmannian-Steinberg quiver flag varieties.…
We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitable for statistical analysis and a setup adopted for…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials…
We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…
We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module…
It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…
The aim of this paper is to study the singularities of certain moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non--generic polarization, with respect…
Transformers serve as the foundation of most modern large language models. To mitigate the quadratic complexity of standard full attention, various efficient attention mechanisms, such as linear and hybrid attention, have been developed. A…
In earlier work, the author classified rigid representations of a quiver by finitely generated free modules over a principal ideal ring. Here we extend the results to representations of a quiver by finitely generated projective modules over…
In this paper we study the persistent current (PC) of a staggered Harper model, close to the half-filling. The Harper model, which is a quasi-periodic system, is different than other one dimensional systems with uncorrelated disorder in the…
Fortin and Reutenauer defined the non-commutative rank for a matrix with entries that are linear functions. The non-commutative rank is related to stability in invariant theory, non-commutative arithmetic circuits, and Edmonds' problem. We…
In this paper, we describe a categorical action of any Kac-Moody algebra on a category of quantized coherent sheaves on Nakajima quiver varieties. By "quantized coherent sheaves," we mean a category of sheaves of modules over a deformation…
In this paper we construct a covariant light-front model of heavy mesons within the framework of heavy quark effective theory (HQET). The covariant model consists of the light-front heavy meson bound states constructed in the heavy quark…
This paper develops a compact, size-aware blueprint for transferring structure through gadget lifts. Two low-order invariants -- cumulative mod-$q$ Fourier mass up to degree $k$ and noise stability $\mathrm{Stab}_\rho$ -- are treated as a…
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…
We consider the localization $\mathcal{Q}_{\mathbf{V},\mathbf{W}}/\mathcal{N}_{\mathbf{V}}$ of Lusztig's sheaves for framed quivers, and define functors $E^{(n)}_{i},F^{(n)}_{i},K^{\pm}_{i},n\in \mathbb{N},i \in I$ between the…
We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…