Related papers: Total positivity criteria for partial flag varieti…

In 2015, Chen, Liang and Wang provided several sufficient conditions for the total positivity of Riordan arrays and asked for combinatorial proofs of these results. In this paper, we present such proofs by constructing suitable planar…

We consider finitely generated normal algebras over an algebraically closed field of characteristic zero that come with a complexity one grading by a finitely generated abelian group such that the conditions of a UFD are satisfied for…

We prove that the total Cartier index of a bounded family of projective varieties of klt type is bounded.

We construct a family of points on the Lagrangian cone of a partial flag bundle associated to a (possibly non-split) vector bundle from any Weyl-invariant $I$-function of a prequotient. This result can be seen as the nonabelian analogue of…

In this paper, we find a criterium for universal equivalence of partially commutative Lie algebras whose defining graphs are trees. Besides, we obtain bases for partially commutative metabelian Lie algebras.

We extend results of Chang and Ran regarding large dimensional families of immersed curves of positive genus in projective space in two directions. In one direction, we prove a sharp bound for the dimension of a complete family of smooth…

The existence of acyclic complete matchings on the face poset of a regular CW complex implies that the underlying topological space of the CW complex is contractible by discrete Morse theory. In this paper, we construct explicitly acyclic…

Let W be a Weyl group. We introduce the notion of positive conjugacy class in W. This generalizes the notion of regular elliptic conjugacy class in the sense of Springer.

Let $G$ be a complex quasi-simple algebraic group and $G/P$ be a partial flag variety. The projections of Richardson varieties from the full flag variety form a stratification of $G/P$. We show that the closure partial order of projected…

We extend Langton's valuative criterion for families of coherent algebraic sheaves to a complex analytic set-up. As a consequence we derive a set of sufficient conditions for the compactness of a moduli space of semistable sheaves over a…

We complete the program for determining the full automorphism groups of all parafermion vertex operator algebras associated with simple Lie algebras and positive integral levels. We show that the full automorphism group of the parafermion…

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…

We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…

We introduce a new fundamental group scheme for varieties defined over an algebraically closed field of positive characteristic and we use it to study generalization of some of C. Simpson's results to positive characteristic. We also study…

The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.

We study the totally nonnegative part of the complete flag variety and of its tropicalization. We show that Lusztig's notion of nonnegative complete flag variety coincides with the flags in the complete flag variety which have nonnegative…

We prove that it is NP-complete to decide whether a given string can be factored into palindromes that are each unique in the factorization.

The totally nonnegative part of a partial flag variety G/P has been shown by the first author to be a union of semi-algebraic cells. Moreover she showed that the closure of a cell is the union of smaller cells. In this note we provide…

We give an effective infinitesimal Torelli theorem for cyclic covers of G/P, where G is a simple algebraic group and P is a maximal parabolic subgroup.

Following the program of algebraic Frobenius splitting begun by Kumar and Littelmann, we use representation-theoretic techniques to construct a Frobenius splitting of the cotangent bundle of the flag variety of a semisimple algebraic group…