Boij-Söderberg theory has had a dramatic impact on commutative algebra. We determine explicit Boij-Söderberg coefficients for ideals with linear resolutions and illustrate how these arise from the usual Eliahou-Kervaire computations for Borel ideals. In addition, we explore a new numerical decomposition for resolutions based on a row-by-row approach; here, the coefficients of the Betti diagrams...

We prove that orbit equivalence relations (ERs, for brevity) of generically turbulent Polish actions are not Borel reducible to ERs of a family which includes Polish actions of S∞, the group of all permutations of N, and is closed under the Fubini product modulo the ideal Fin of all finite sets, and some other operations. Our second main result shows that T2, an equivalence relation called “the...

Let g be a complex simple Lie algebra, with fixed Borel subalgebra b⊂g and Weyl group W. Expanding on previous work of Fan Stembridge in the simply laced case, this note aims to study fully commutative elements W, their connections spherical nilpotent orbits g. If is not type G2, it shown that an element w∈W if only b determined by inversions w lies closure orbit. A similar characterization als...

Let $\mathfrak {g}$ be a complex simple Lie algebra. We classify the parabolic subalgebras {p}$ of such that nilradical has commutative polarisation. The answer is given in terms Kostant cascade. It requires also notion an optimal and some properties abelian ideals Borel subalgebra .

We show that the regularity of monomial ideals of K[x1, . . . , xn] (K being a field), whose associated prime ideals are totally ordered by inclusion is upper bounded by a linear function in n.