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...

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 in that 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 ...

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...

The archimedean Euler factor in the completed spin L–function of a Siegel modular form is computed. Several formulas are obtained, relating this factor to the recursively defined factors of Andrianov and to symmetric power L–factors for GL(2). The archimedean ε–factor is also computed. Finally, the critical points of certain motives in the sense of Deligne are determined. Introduction Let f be ...

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.

There is a natural analytification functor from the category of locally separated algebraic spaces locally of finite type over C to the category of complex-analytic spaces [Kn, Ch. I, 5.17ff]. (Recall that a map of algebraic spaces X → S is locally separated if the diagonal ∆X/S : X → X ×S X is an immersion. We require algebraic spaces to have quasi-compact diagonal over SpecZ.) It is natural t...

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)/ ∑

Formulae for the number of branch points of one-dimensional orbifolds defined over a non-archimedean local field and uniformisable by discrete projective linear groups are given. They depend only on the uniformising group. The method of equivariant pasting reveals the possible relative position of the branch points.

Let F be a non-Archimedean local field and let E be a finite extension of F . Let G be an F -split semisimple F -group. We discuss how to compare volumes on the Bruhat–Tits buildings BE and BF of G(E) and G(F ) respectively.