Abstract Involution Schubert polynomials represent cohomology classes of K -orbit closures in the complete flag variety, where is orthogonal or symplectic group. We show they also $\mathsf {T}$ -equivariant subvarieties defined by upper-left rank conditions spaces symmetric skew-symmetric matrices. This geometry implies that these are positive combinations monomials variables $x_i + x_j$ , and ...

We have investigated the role of IL-6 in the initiation and progression of mouse mammary gland involution in IL-6-null mice. This study was based on the hypothesis that IL-6 is the activating cytokine for signal transducer and activator of transcription 3 (Stat), the transcription factor whose presence is required for controlled mammary gland involution. We now show that expression of IL-6 is l...

We define an invariant of torsors under adjoint linear algebraic groups of type Cn—equivalently, central simple algebras of degree 2n with symplectic involution—for n divisible by 4 that takes values in H(k, μ2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple alg...

Involution is the process of post-lactational mammary gland regression to quiescence and it involves secretory epithelial cell death, stroma remodeling and gland repopulation by adipocytes. Though reportedly accompanying apoptosis, the role of autophagy in involution has not yet been determined. We now report that autophagy-related (ATG) proteins mediate dead cell clearance and suppress inflamm...

Recent pregnancy correlates with decreased survival for breast cancer patients compared with non-pregnancy-associated breast cancer. We hypothesize that postpartum mammary involution induces metastasis through wound-healing programs known to promote cancer. It is unknown whether alternatively activated M2 macrophages, immune cells important in wound-healing and experimental tumorigenesis that a...

Mammary gland involution is a physiological process that follows lactation and results in the rapid disappearance of the entire lobulo-alveolar compartment. Coincident with the onset of involution, milk protein gene expression ceases and alveolar cells undergo programmed cell death. In mammary epithelial tissue culture cells in vitro, both p53-dependent and p53-independent apoptosis pathways ha...

Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...

Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...

A formula is given for the discriminant of the tensor product of the canonical involution on a quaternion algebra and an orthogonal involution on a central simple algebra of degree divisible by 4. As an application, an alternative proof of Shapiro’s “Pfister Factor Conjecture” is given for tensor products of at most five quaternion algebras. Throughout this paper, the characteristic of the base...