Related papers: Shelling totally nonnegative flag varieties

We determine the homeomorphism type of the space of smooth complete nonnegatively curved metrics on surfaces of positive Euler characteristic equipped with the topology of $C^\gamma$ uniform convergence on compact sets, when $\gamma$ is…

We classify the GL_p x GL_q-orbits in the flag variety for GL_{p+q} with rationally smooth closure, showing that they are all either already closed or are pullbacks from orbits with smooth closure in a partial flag variety.

By a theorem of A.Bj\"orner, for every interval $[u,v]$ in the Bruhat order of a Coxeter group $W$, there exists a stratified space whose strata are labeled by the elements of $[u,v]$, adjacency is described by the Bruhat order, and each…

We examine the partition of a finite Coxeter group of type $B$ into cells determined by a weight function $L$. The main objective of these notes is to reconcile Lusztig's description of constructible representations in this setting with…

Motivated by the observation that groups can be effectively studied using metric spaces modelled on $\ell^1$, $\ell^2$, and $\ell^\infty$ geometry, we consider cell complexes equipped with an $\ell^p$ metric for arbitrary $p$. Under weak…

Suppose that $W$ is a finite Coxeter group and $W_J$ a standard parabolic subgroup of $W$. The main result proved here is that for any for any $w \in W$ and reduced expression of $w$ there is an Elnitsky tiling of a $2m$-polygon, where $m =…

In this article, we discuss the spaces of harmonic forms $\mathcal{H}^{\bullet}_{d}$ over a closed almost K\"{a}hler manifold $(X, J,\omega)$. We show that if the almost complex structure $J$ on the almost K\"{a}hler manifold $X$ is not too…

Let $G$ be a finitely generated Kleinian group and let $\Delta$ be an invariant collection of components in its region of discontinuity. The Teichm\"uller space $T(\Delta,G)$ supported in $\Delta$, is the space of equivalence classes of…

We relate the semiclassical asymptotics of the 6j symbols for the representation theory of the quantized enveloping algebra U_q(sl_2) at q a primitive root of unity, or q positive real, to the geometry of non-Euclidean tetrahedra. The…

We present a comprehensive study of the degeneracy loci of the full flag varieties of all complex semisimple Lie groups equipped with the standard Poisson structures. The reduced Poisson degeneracy loci are shown to stratify under the…

We prove a conjecture of Thomas Lam that the face posets of stratified spaces of planar resistor networks are shellable. These posets are called uncrossing partial orders. This shellability result combines with Lam's previous result that…

We compute the Euler characteristics of quiver Grassmannians and quiver flag varieties of tree and band modules and prove their positivity. This generalizes some results by G.C. Irelli [arXiv:0910.2592]. As an application we consider the…

Let De_n be the simplicial complex of squarefree positive integers less than or equal to n ordered by divisibility. It is known that the asymptotic rate of growth of its Euler characteristic (the Mertens function) is closely related to deep…

We study the structure of a Leibniz triple system $\mathcal{E}$ graded by an arbitrary abelian group $G$ which is considered of arbitrary dimension and over an arbitrary base field $\mathbb{K}$. We show that $\mathcal{E}$ is of the form…

Let K be a CM-field, i.e., a totally complex quadratic extension of a totally real field F. Let X be a g-dimensional abelian variety admitting an algebra embedding of F into the rational endomorphisms of X. Let A be the product of X and…

Let G be a connected complex semisimple Lie group. Webster and Yakimov have constructed partitions of the double flag variety G/B x G/B_, where (B, B_) is a pair of opposite Borel subgroups of G, generalizing the Deodhar decompositions of…

The goal of this paper is twofold. First, we write down the semi-infinite Pl\"ucker relations, describing the Drinfeld-Pl\"ucker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous…

Each choice of a K\"ahler class on a compact complex manifold defines an action of the Lie algebra $\slt$ on its total complex cohomology. If a nonempty set of such K\"ahler classes is given, then we prove that the corresponding…

We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic…

In this paper we construct some quantum analogues of the global Cousin complex for the flag variety in positive characteristic. Just like in the positive characteristic case, we obtain some remarkable resolutions of the contragradient…