The Lipschitz Saturation of a Module

Infinitesimal Lipschitz conditions on family of analytic varieties

In this work, we extend the concept of the double of an ideal defined in \cite{G2}, to the context of modules. We also obtain the genericity of the infinitesimal Lipschitz condition A for an enlarged class of analytic spaces.

分支规则的饱和性质--实例

The saturation property for branching rules -- Examples

对于少数可约群对$G\subset \hat G$，研究了不可约$\hait G$ -模到$G$ -模的分解.特别是，我们观察到所有这些对的饱和特性。

Weight polytopes and saturation of Demazure characters

For $G$ a reductive group and $T\subset B$ a maximal torus and Borel subgroup, Demazure modules are certain $B$-submodules, indexed by elements of the Weyl group, of the finite irreducible representations of $G$. In order to describe the $T$-weight spaces that appear in a Demazure module, we study the convex hull of these weights - the Demazure polytope. We characterize these polytopes both by vertices and by inequalities, and we use these results to prove that Demazure characters are saturated, in the case that $G$ is simple of classical Lie type. Specializing to $G=GL_n$, we recover results …

What makes a complex a virtual resolution?

Virtual resolutions are homological representations of finitely generated $\text{Pic}(X)$-graded modules over the Cox ring of a smooth projective toric variety. In this paper, we identify two algebraic conditions that characterize when a chain complex of graded free modules over the Cox ring is a virtual resolution. We then turn our attention to the saturation of Fitting ideals by the irrelevant ideal of the Cox ring and prove some results that mirror the classical theory of Fitting ideals for Noetherian rings.