In the first part of the paper we generalize a descent technique due to HarishChandra to the case of a reductive group acting on a smooth affine variety both defined over arbitrary local field F of characteristic zero. Our main tool is Luna slice theorem. In the second part of the paper we apply this technique to symmetric pairs. In particular we prove that the pair (GLn(C), GLn(R)) is a Gelfan...

For a point O on the segment AB in the plane, the area surrounded by the three semicircles with diameters AO, BO and AB erected on the same side is called an arbelos. It has lots of unexpected but interesting properties (for an extensive reference see [1]). The radical axis of the inner semicircles divides the arbelos into two curvilinear triangles with congruent incircles called the twin circl...

in the present paper, we give a new approach to caristi's fixed pointtheorem on non-archimedean fuzzy metric spaces. for this we define anordinary metric $d$ using the non-archimedean fuzzy metric $m$ on a nonemptyset $x$ and we establish some relationship between $(x,d)$ and $(x,m,ast )$%. hence, we prove our result by considering the original caristi's fixedpoint theorem.

We consider the problem of counting polynomial curves on analytic or definable subsets over field C((t)) as a function degree r. A result this type could be expected by analogy with classical Pila–Wilkie theorem in Archimedean situation. Some non-Archimedean analogues have been developed work Cluckers, Comte, and Loeser for Qp, but situation appears to significantly different. prove that set fi...

A set is called a unique range set for a certain class of functions if each inverse image of that set uniquely determines a function from the given class. We show that a finite set is a unique range set, counting multiplicity, for non-Archimedean entire functions if and only if there is no non-trivial affine transformation preserving the set. Our proof uses a theorem of Berkovich to extend, to ...

Let F be a non-Archimedean locally compact field, let G be a split connected reductive group over F . For a parabolic subgroup Q ⊂ G and a ring L we consider the G-representation on the L-module (∗) C∞(G/Q, L)/ ∑

In the title compound, [Hf(C(15)H(11)O(2))(4)], the Hf(IV) atom is coordinated by four 1,3-diphenyl-propane-1,3-dionato ligands with an average Hf-O distance of 2.17 (3) Å and O-Hf-O bite angles varying from 74.5 (1) to 75.02 (9)°. The coordination polyhedron shows a slightly distorted Archimedean square-anti-prismatic geometry. The crystal packing is stabilized by weak C-H⋯O inter-actions.

Let $$\pi _1$$ be a standard representation of $$\textrm{GL}_{n+1}(F)$$ and let _2$$ the smooth dual $$\textrm{GL}_n(F)$$ . When F is non-Archimedean, we prove that $$\textrm{Ext}^i_{\textrm{GL}_n(F)}(\pi _1, \pi _2)$$ $$\cong \mathbb {C}$$ when $$i=0$$ vanishes $$i \ge 1$$ The main tool proof notion left right Bernstein–Zelevinsky filtrations. An immediate consequence result to give new on mul...

Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is uniformly Archimedean then it is sharply dominating.

Measures with values in non-Archimedean fields, which are quasi-invariant and descending at infinity on topological vector spaces over non-Archimedean fields, are studied in this paper. Moreover, their characteristic functionals are considered. In particular, measures having convolution properties like classical Gaussian measures are investigated in the paper. Applications of such measures to p...