Related papers: Category $\mathcal{O}$ and asymptotic characters
Higher Lie characters form a distinguished family of symmetric group characters, which appear in many areas of algebra and combinatorics. An old open problem of Thrall is to decompose them into irreducibles. We propose a novel asymptotic…
Given a local Haag-Kastler net of von Neumann algebras and one of its scaling limit states, we introduce a variant of the notion of asymptotic morphism by Connes and Higson, and we show that the unitary equivalence classes of (localized)…
Let $\mathfrak{X}$ be a formal smooth curve over a complete discrete valuation ring of mixed characteristic and let $\mathfrak{X}\_K$ be its generic fiber. We consider respectively over $\mathfrak{X}$ and $\X\_K$ the sheaves of differential…
Michael Gromov has recently initiated what he calls ``symbolic algebraic geometry", in which objects are proalgebraic varieties: a proalgebraic variety is by definition the projective limit of a projective system of algebraic varieties. In…
In this article we study a differential algebra of modular-type functions attached to the periods of a one parameter family of Calabi-Yau varieties which is mirror dual to the universal family of quintic threefolds. Such an algebra is…
In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young…
We introduce the notion of asymptotic Grothendieck groups for abelian and triangulated categories that are both AB4 and AB4*. We study when the asymptotic Grothendieck group of the heart of a triangulated category with a t-structure is…
There are two abelian groups which can naturally be associated to an additive category A: the split Grothendieck group of A and the triangulated Grothendieck group of the homotopy category of (bounded) complexes in A. We prove that these…
We introduce asymptotic-M\"obius (AM) maps, a large-scale analogue of quasi-M\"obius maps tailored to geometric group theory. AM-maps capture coarse cross-ratio behavior for configurations of points that lie far apart, providing a notion of…
We provide an algorithm to classify the asymptotic sets of the dominant polynomial mappings $F: \C^3 \to \C^3$ of degree 2, using the definition of the so-called "{\it fa\c{c}ons}" in \cite{Thuy}. We obtain a classification theorem for the…
We give explicit computations of the $\Gamma$-Euler characteristic of several families of orbit space definable translation groupoids. These include the translation groupoids associated to finite-dimensional linear representations of the…
We develop a saddle-point theory for acyclic orientations and negative chromatic evaluations of complete multipartite graphs, with applications to OEIS A267383, A372326, A372084, A372395, and A370613. The main tool is an exact Gamma-type…
We study the interplay between noncommutative tori and noncommutative elliptic curves through a category of equivariant differential modules on $\mathbb{C}^*$. We functorially relate this category to the category of holomorphic vector…
The quantum Grothendieck ring of a certain category of finite-dimensional modules over a quantum loop algebra associated with a complex finite-dimensional simple Lie algebra $\mathfrak{g}$ has a quantum cluster algebra structure of…
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary…
We equip the categorified quantum group attached to a KLR algebra and an arbitrary choice of scalars with duality functor which is cyclic, that is, such that f=f^** for all 2-morphisms f. This is accomplished via a modified diagrammatic…
We study the prefundamental modules $L_{s,a}^{\pm}$ over the Borel subalgebras of the twisted quantum loop algebras, which are introduced by Wang. A character formula for $L_{s,a}^{\pm}$ is obtained from that for the prefundamental modules…
We show that the typical coordinate-wise encoding of multivariate ergodic source into prescribed alphabets has the entropy profile close to the convolution of the entropy profile of the source and the modular polymatroid that is determined…
We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…
We introduce a new algebraic-cycle model for the motivic cohomology theory of truncated polynomials $k[t]/(t^m)$ in one variable. This approach uses ideas from the deformation theory and non-archimedean analysis, and is distinct from the…