Related papers: Cambrian fans
As an alternative to the description of a toric variety by a fan in the lattice of one parameter subgroups, we present a new language in terms of what we call bunches -- these are certain collections of cones in the vector space of rational…
This paper shows the polytopality of any finite type $\mathbf{g}$-vector fan, acyclic or not. In fact, for any finite Dynkin type $\Gamma$, we construct a universal associahedron $\mathsf{Asso}_{\mathrm{un}}(\Gamma)$ with the property that…
We introduce a new cluster character with coefficients for a cluster category $\mathcal{C}$ and rather than using a Frobenius $2$-Calabi-Yau realization to incorporate coefficients into the representation-theoretic model for a cluster…
For a toric variety X_P determined by a rational polyhedral fan P in a lattice N, Payne shows that the equivariant Chow cohomology of X_P is the Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use the…
The main goal of this paper is to give explicit descriptions of two maximal cones in the Gr\"obner fan of the Pl\"ucker ideal. These cones correspond to the monomial ideals given by semistandard and PBW-semistandard Young tableaux. For the…
Faber, Muller and Smith used complete sums of conic modules to construct non-commutative crepant resolutions (NCCR) of simplicial toric algebras. We link these conic modules to the Bondal-Thomsen collection of line bundles on smooth toric…
Tropical algebraic geometry is the geometry of the tropical semiring (R, min, +). The theory of total positivity is a natural generalization of the study of matrices with all minors positive. In this paper we introduce the totally positive…
Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid.…
We study the stable category of the factor algebra of the preprojective algebra associated with an element $w$ of the Coxeter group of a quiver. We show that there exists a silting object $M(\bf{w})$ of this category associated with each…
We study a bilayer GaAs hole system that hosts two distinct many-body phases at low temperatures and high perpendicular magnetic fields. The higher-density (top) layer develops a Fermi sea of composite fermions (CFs) in its half-filled…
An exchange matrix $B$ dominates an exchange matrix $B'$ if the signs of corresponding entries weakly agree, with the entry of $B$ always having weakly greater absolute value. When $B$ dominates $B'$, interesting things happen in many cases…
The purpose of this paper is to show that the reflex fields of a given CM-field is equipped with a certain combinatorial structure that has not been exploited yet. We prove three theorems using this structure; the first theorem is on the…
The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any…
A Coxeter system is an ordered pair (W,S) where S is the generating set in a particular type of presentation for the Coxeter group W. A subgroup of W is called special if it is generated by a subset of S. Amalgamated product decompositions…
For a finite dimensional algebra $A$ over a field $k$, the 2-term silting complexes of $A$ gives a simplicial complex $\Delta(A)$ called the $g$-simplicial complex. We give tilting theoretic interpretations of the $h$-vectors and…
We investigate C^*-algebras generated by scaling elements. We generalize the Wold decomposition and Coburn's theorem on isometries to scaling elements. We also completely determine when the C^*-algebra generated by a scaling element…
We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in…
Let $Q$ be an acyclic quiver and $\mathbf{s}$ be a sequence with elements in the vertex set $Q_0$. We describe an induced sequence of simple (backward) tilting in the bounded derived category $\mathcal{D}(Q)$, starting from the standard…
In this paper, I will present the recent progress on circular-ribbon flares (CRFs) and their related activities, including coronal jets, filaments, CMEs, radio bursts, coronal dimmings, and coronal loop oscillations. Owing to the prevalence…
Let B be a real hyperplane arrangement which is stable under the action of a Coxeter group W. Then B acts naturally on the set of chambers of B. We assume that B is disjoint from the Coxeter arrangement A=A(W) of W. In this paper, we show…