相关论文: Dynkin diagram sequences and stabilization phenome…

In this note we make explicit a stability property for Kronecker coefficients that is implicit in a theorem of Y. Dvir. Even in the simplest nontrivial case this property was overlooked despite of the work of several authors. As an…

In 1980 Lusztig proved a stabilisation property of the affine Kazhdan-Lusztig polynomials. In this paper we give a categorical version of such a result using the theory of sheaves on moment graphs. This leads us to associate with any…

Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Monadically stable classes, originating from model theory,…

We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually…

We establish a crossed product decomposition theorem for stabilized Cuntz--Pimsner algebras. This result extends Cuntz's classical decomposition for the Cuntz algebras $\mathcal{O}_n$ and reveals an implicit symmetric structure within…

In this paper, we describe a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert…

We study the representation theory of Dynkin quivers of type A in abstract stable homotopy theories, including those associated to fields, rings, schemes, differential-graded algebras, and ring spectra. Reflection functors, (partial)…

In this article, we treat stability conditions in the sense of King, Bridgeland and Bayer in a single framework. Following King, we begin with weight functions on a triangulated category, and consider increasingly specialised configurations…

Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a…

We investigate a class of Kac-Moody algebras previously not considered. We refer to them as n-extended Lorentzian Kac-Moody algebras defined by their Dynkin diagrams through the connection of an $A_n$ Dynkin diagram to the node…

The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic…

For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…

We introduce a notion of uniform Ding stability for a projective manifold with big anticanonical class, and prove that the existence of a unique K\"ahler-Einstein metric on such a manifold implies uniform Ding stability. The main new…

This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…

We present a classification of characteristic Dynkin diagrams for the $A_N$, $B_N$, $C_N$ and $D_N$ algebras. This classification is related to the classification of \cw(\cg,\ck) algebras arising from non-Abelian Toda models, and we argue…

In this paper we introduce a new property for normed algebras. This property which we call it stability, plays a key role in the studying of the theory of almost multiplier maps. In this note we study some of the basic properties of this…

We consider stable representations of non-Dynkin quivers with respect to a central charge. On one condition the existence of a stable representation with self-extensions implies the existence of infinitely many stables without…

We present the theory of non-stationary normal forms for uniformly contracting smooth extensions with sufficiently narrow Mather spectrum. We give coherent proofs of existence, (non)uniqueness, and a description of the centralizer results.…

The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…

We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory. This leads to an axiomatic notion of a central charge on a scheme with…