Related papers: Bruhat order for two flags and a line

Let G be the split special orthogonal group of degree 2n+1 over a field F of char F \ne 2. Then we describe G-orbits on the triple flag varieties G/P\times G/P\times G/P and G/P\times G/P\times G/B with respect to the diagonal action of G…

A Steiner quadruple system of order v is a 3-(v,4,1) design, and will be denoted SQS(v). Using the classification of finite 2-transitive permutation groups all SQS(v) with a flag-transitive automorphism group are completely classified, thus…

Let $M$ and $N$ be modules over an artin algebra such that $M$ degenerates to $N$. We show that any submodule of $M$ degenerates to a submodule of $N$. This suggests that a composition series of $M$ will in some sense degenerate to a…

In this paper, we introduce tree varieties as a natural generalization of products of partial flag varieties. We study orbits of the PGL action on tree varieties. We characterize tree varieties with finitely many PGL orbits, generalizing a…

Consider a one-parameter family of smooth projective varieties X_t which degenerate into a simple normal crossing divisor at t=0. What is the dual variety in the limit? We answer this question for a hypersurface of degree d degenerate to…

We investigate the nondegeneracy of higher order Levi forms on weakly nondegenerate homogeneous $CR$ manifolds. Improving previous results, we prove that general orbits of real forms in complex flag manifolds have order less or equal $3$…

We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen-Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry,…

Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate…

In this paper, we study the deformation theory of degenerate algebraic curves on singular varieties which appear as the degenerate limit of families of varieties. For this purpose, we systematically develop a new method to calculate the…

Frustration in classical spin models can lead to degenerate ground states without long range order. In reciprocal space, these degeneracies appear as manifolds of wave vectors, their dimensionality increasing with the degree of frustration…

We show that the principal order ideal below an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are…

A triality is a sort of super-symmetry that exchanges the types of the elements of an incidence geometry in cycles of length three. Although geometries with trialities exhibit fascinating behaviors, their construction is challenging, making…

A conventional periodic LC ladder circuit forms a transmission line that has a regular band edge between a pass and a stop band. Here for the first time we develop the theory of simple yet unconventional double ladder circuit that exhibits…

We study toric degenerations of opposite Schubert and Richardson varieties inside degenerations of Grassmannians and flag varieties. These degenerations are parametrized by matching fields in the sense of Sturmfels and Zelevinsky. We…

A line bundle on a curve with two marked points can be special in many ways, as measured by the global sections of all of its twists by these points. All of this information is conveniently packaged into a permutation, which we call the…

In [BFMT17] we introduced orbital degeneracy loci as generalizations of degeneracy loci of morphisms between vector bundles. Orbital degeneracy loci can be constructed from any stable subvariety of a representation of an algebraic group. In…

We derive a formula for the entries in the change-of-basis matrix between Young's seminormal and natural representations of the symmetric group. These entries are determined as sums over weighted paths in the weak Bruhat graph on standard…

We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the…

We illuminate the relation between the Bruhat order on the symmetric group and structure constants (Littlewood-Richardson coefficients) for the cohomology of the flag manifold in terms of its basis of Schubert classes. Equivalently, the…

Let $k$ be an algebraically closed field and $\alpha$, $\beta$, $\gamma$ be partitions. An algebraic group acts on the constructible set of short exact sequences of nilpotent $k$-linear operators of Jordan types $\alpha$, $\beta$, and…