Related papers: Branching integrals and Casselman phenomenon

Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex…

Deformation K-theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2-periodic above the rational cohomological dimension of G…

Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…

In the paper we prove a factorization theorem for representations of fundamental groups of compact K\"{a}hler manifolds ({\em K\"{a}hler groups}) into solvable matrix groups. We apply this result to prove that the universal covering of a…

Let $G$ be an algebraic group, $X$ a generically free $G$-variety, and $K=k(X)^G$. A field extension $L$ of $K$ is called a splitting field of $X$ if the image of the class of $X$ under the natural map $H^1(K, G) \mapsto H^1(L, G)$ is…

The unitary principal series representations of $G=GL(n,\mathbb{C})$ induced from a character of the maximal parabolic subgroup $P=(GL(1,\mathbb{C})\times GL(n-1,\mathbb{C}))\ltimes\mathbb{C}^{n-1}$ attain the minimal Gelfand--Kirillov…

In this paper we study holomorphic actions of the complex multiplicative group on complex manifolds around a singular (fixed) point. We prove linearization results for the germ of action and also for the whole action under some conditions…

The ring of invariant polynomials ${\mathbb C}[V]^G$ over a given finite dimensional representation space $V$ of a complex reductive group $G$ is known, by a famous theorem of Hilbert, to be finitely generated. The general proof being…

Fix a non-negative integer g and a positive integer I dividing 2g-2. For any Henselian, discretely valued field K whose residue field is perfect and admits a degree I cyclic extension, we construct a curve C over K of genus g and index I.…

The holomorph of a discrete group $G$ is the universal semi-direct product of $G$. In chapter 1 we describe why it is an interesting object and state main results. In chapter 2 we recall the classical definition of the holomorph as well as…

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain $V\oplus i\Omega$ that are obtained by analytic continuation of the holomorphic discrete series. For a representation…

Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…

We prove an extension of a theorem of A.Ros on a characterization of seven compact Kaehler submanifolds by holomorphic pinching to certain submanifolds of the complex Grassmannian manifolds.

Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using…

We consider the generalized Segal-Bargmann transform C_t for a compact group K, introduced in B. C. Hall, J. Funct. Anal. 122 (1994), 103-151. Let K_C denote the complexification of K. We give a necessary-and-sufficient pointwise growth…

Consider a restriction of an irreducible finite dimensional holomorphic representation of $\GL(n+1,C)$ to the subgroup $GL(n,C)$ (it is determined by the Gelfand-Tsetlin branching rule). We write explicitly formulas for generators of the…

Let $k$ be an algebraically closed field of characteristic two, and let $G$ be isomorphic to $\mathbb{Z}/2\times\mathbb{Z}/2$. Suppose $X$ is a smooth projective irreducible curve over $k$ with a faithful $G$-action, and assume that the…

In this work, the continuously controlled assembly map in algebraic $K$-theory, as developed by Carlsson and Pedersen, is proved to be a split injection for groups $\Gamma$ that satisfy certain geometric conditions. The group $\Gamma$ is…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

Developing ideas of \cite{Fei}, we introduce canonical cosimplicial cohomology of meromorphic functions for infinite-dimensional Lie algebra formal series with prescribed analytic behavior on domains of a complex manifold $M$. Graded…