The notion of “Weierstrass Section”, comes from Weierstrass canonical form for elliptic curves. In celebrated work Kostant (1963) [26] constructed such a section the action semisimple Lie algebra on its dual using principal s-triple. Actually it is enough to have an “adapted pair” and indeed construction in Joseph Shafrir (2010) [25] works rather well co-adjoint algebraic, but not necessarily r...

In the cohomology ring of an extraspecial p-group, the subring generated by Chern classes and transfers is studied. This subring is strictly larger than the Chern subring, but still not the whole cohomology ring, even modulo nilradical. A formula is obtained relating Chern classes to transfers. Introduction Methods to determine the cohomology ring of a finite group almost always presuppose that...

In this paper, we consider a connected Riemannian manifold $M$ where Lie group $G$ acts effectively and isometrically. Assume $X\in\mathfrak{g}=\mathrm{Lie}(G)$ defines bounded Killing vector field, find some crucial algebraic properties of the decomposition $X=X_r+X_s$ according to Levi $\mathfrak{g}=\mathfrak{r}(\mathfrak{g})+\mathfrak{s}$, $\mathfrak{r}(\mathfrak{g})$ is radical, $\mathfrak{...

Let G be a semisimple Lie group and let g = n− + h+ n be a triangular decomposition of g = LieG. Let b = h+ n and let H, N, B be Lie subgroups of G corresponding respectively to h, n and b. We may identify n− with the dual space to n. The coadjoint action of N on n− extends to an action of B on n−. There exists a unique nonempty Zariski open orbit X of B on n−. Any N -orbit in X is a maximal co...

It is proven that each indecomposable injective module over a valuation domain R is polyserial if and only if each maximal immediate extension R̂ of R is of finite rank over the completion R̃ of R in the R-topology. In this case, for each indecomposable injective module E, the following invariants are finite and equal: its Malcev rank, its Fleischer rank and its dual Goldie dimension. Similar res...

In this diagram, G is a connected complex semisimple group of adjoint type with Lie algebra g. We fix a Borel subgroup B ⊂ G, write b = Lie B ⊂ g for the corresponding Borel subalgebra, and n for the nilradical of b. Let Ñ := G×B n be the Springer resolution, and CohG×C ∗ (Ñ ) the abelian category ofG×C∗-equivariant coherent sheaves on Ñ , where the group G acts on Ñ by conjugation and C∗ acts ...

Let f! = G/K be a symmetric tube domain where G is the universal cover of Aut(f!). Let X be a line bundle on the Shilov boundary, and let I(x) be the space of sections. This paper determines (a) the composition series for I(x) as a ({1, K)module, (b) the K-module structure of each constituent, (c) explicit formulas for possible invariant Hermitian forms on these constituents, and (d) the unitar...

If R̂ is the pure-injective hull of a valuation ring R, it is proved that R̂ ⊗R M is the pure-injective hull of M , for every finitely generated Rmodule M . Moreover R̂ ⊗R M ∼= ⊕1≤k≤nR̂/AkR̂, where (Ak)1≤k≤n is the annihilator sequence of M . The pure-injective hulls of uniserial or polyserial modules are also investigated. Any two pure-composition series of a countably generated polyserial module a...