Related papers: Complex crystallographic reflection groups and Sei…
We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin $s=\{0,\frac{1}{2},1,\frac{3}{2},2\}$ we classify and construct all SL(2,$\mathbb{C}$) primary…
The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite root system considered. Although the irreducible modules…
In this paper, we use the theory of algebraic groups to prove a number of new and fundamental results about the orthogonal Gelfand-Zeitlin system. We show that the moment map (orthogonal Kostant-Wallach map) is surjective and simplify…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
We show that the $m$-dimensional Euler--Manakov top on $so^*(m)$ can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety $\bar{\cal V}(k,m)$, and present its Lax representation…
In this paper, we study Coxeter systems with two-dimensional Davis-Vinberg complexes. We show that for a Coxeter group $W$, if $(W,S)$ and $(W,S')$ are Coxeter systems with two-dimensional Davis-Vinberg complexes, then there exists…
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 introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the…
We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of…
In this paper, we give a new class of rigid Coxeter groups. Let $(W,S)$ be a Coxeter system. Suppose that (0) for each $s,t\in S$ such that $m(s,t)$ is even, $m(s,t)\in\{2\}\cup 4\N$, (1) for each $s\neq t\in S$ such that $m(s,t)$ is odd,…
Ehrenborg and Jung recently related the order complex for the lattice of d-divisible partitions with the simplicial complex of pointed ordered set partitions via a homotopy equivalence. The latter has top homology naturally identified as a…
We study the crystal graphs of irreducible $U_{v}(\hat{sl}}_{e})$-modules of higher level l. Generalizing works of the first author, we obtain a simple description of the bijections between the classes of multipartitions which naturally…
We determine semisimple reductions of irreducible, 2-dimensional crystalline representations of the absolute Galois group $\text{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_{p^f})$. To this end, we provide explicit representatives for the…
The classification of 4d $\mathcal{N}=2$ SCFTs boils down to the classification of conical special geometries with closed Reeb orbits (CSG). Under mild assumptions, one shows that the underlying complex space of a CSG is (birational to) an…
Argyres and co-workers started a program to classify all 4d $\mathcal{N}=2$ QFT by classifying Special Geometries with appropriate properties. They completed the program in rank-1. Rank-1 $\mathcal{N}=2$ QFT are equivalently classified by…
Let $W$ be a complex reflection group. We formulate a conjecture relating blocks of the corresponding restricted rational Cherednik algebras and Rouquier families for cyclotomic Hecke algebras. We verify the conjecture in the case that $W$…
In this work, we study the Willmore submanifolds in a closed connected Riemannian manifold which are orbits for the isometric action of a compact connected Lie group. We call them homogeneous Willmore submanifolds or Willmore orbits. The…
In our recent works we have used meromorphic differentials on Riemann surfaces all of whose periods are real to study the geometry of the moduli spaces of Riemann surfaces. In this paper we survey the relevant constructions and show how…
This letter continues the program aimed at analysis of the scalar product of states in the Chern-Simons theory. It treats the elliptic case with group SU(2). The formal scalar product is expressed as a multiple finite dimensional integral…
We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.