Let G be a semisimple algebraic group over an algebraically closed field of positive characteristic. In this note, we show that an irreducible closed subvariety of the flag variety of G is compatibly split by the unique canonical Frobenius splitting if and only if it is a Richardson variety, i.e. an intersection of a Schubert and an opposite Schubert variety.

For a complex Lie group $G$ with real form $G_0\subset G$, we prove that any Hamiltionian automorphism $\phi$ of coadjoint orbit $\mathcal O_0$ $G_0$ whose connected components are simply connected, may be approximated by holomorphic O_0$-invariant symplectic the corresponding in sense Carleman, provided O$ is closed. In course proof, establish Hamiltonian density property for closed orbits all...

‎in this paper we give a new condition for a sylow $p$-subgroup of a finite group to control transfer‎. ‎then it is deduced a characteri-zation of supersoluble groups that can be seen as a generalization of the well known result concerning the supersolubility of finite groups with cyclic sylow subgroups‎. moreover a condition for a normal embedding of a strongly closed $p$-subgroup is given‎. ...

For G a locally compact abelian group, any closed invariant proper subalgebra of CQ(G) has analytic discs in its spectrum. Related results are given for A(G) and B(G). For a compact group G it is an easy consequence of Bishop's generalized Stone-Weierstrass theorem and some well-known facts on representations that a proper (doubly) invariant uniform algebra on G cannot have G as its spectrum. (...

‎Let $X=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n\‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...

Let G be a compact connected Lie group and let K closed subgroup of G. In this paper, we study whether the functional

Proof. [Solution due to Claudiu Raicu] Consider two polynomials f, g ∈ C[X±] such that the spherical graphs they determine intersect transversely at the points where the vectors vi intersect the sphere. This implies that T (f) and T (g) intersect transversely ([1]) at each point and T (f)∩T (g) = Σ. Using the Transverse Intersection Lemma (lemma 3.2, corollary 3.3 of [1]) we get that Σ = T (f, ...

Let G be a graph with an ordered set of vertices and maximum degree ∆. The domination number γ(G) of G is the minimum order of a set S of vertices such that each vertex not in S is adjacent to some vertex in S. Equivalently, we can label the vertices from {0, 1} so that the sum over each closed neighborhood is at least one; the minimum value of the sum of all labels, with this restriction, is t...

Let B (resp. K , BC , K C ) denote the set of all nonempty bounded (resp. compact, bounded convex, compact convex) closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B stand for the set of all F ∈ B such that the problem (F,G) is well-posed. We proved that, if X is strictly convex and Kadec, the set ...

Let (M, g) be a closed Riemannian manifold of dimension n ≥ 3 and let f ∈ C∞(M), such that the operator Pf := ∆g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of Pf as the constant term in the expansion of the Green function of Pf at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n−2 4(n−1) sg, ...