Related papers: Group Actions on Riemann-Roch Space

Let $G$ be a split reductive group over a local field $\bK$, and let $G((t))$ be the corresponding loop group. In \cite{GK} we have introduced the notion of a representation of (the group of $\bK$-points) of $G((t))$ on a pro-vector space.…

The automorphism group $Aut(X,\mu)$ of a compact, complete metric space $X$ with a Radon measure $\mu$ is a subgroup of $\mathcal{U}(L^2(X,\mu))$-the unitary group of operators on $L^2(X,\mu)$. The $Aut(X,\mu)$-action on the generalized…

We construct the most general local effective actions for Goldstone boson fields associated with spontaneous symmetry breakdown from a group $G$ to a subgroup $H$. In a preceding paper, it was shown that any $G$-invariant term in the…

For an (imaginary) hyperelliptic curve $\mathcal{H}$ of genus $g$, we determine a basis of the Riemann-Roch space $\mathcal{L}(D)$, where $D$ is a divisor with positive degree $n$, linearly equivalent to $P_1+\cdots+ P_j+(n-j)\Omega$, with…

Deformation spaces Hom($\pi$,G)/G of representations of the fundamental group $\pi$ of a surface $\Sigma$ in a Lie group $G$ admit natural actions of the mapping class group $Mod_\Sigma$, preserving a Poisson structure. When $G$ is compact,…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

We explicitly construct a finite set of separating invariants for the basic $\Ga$-actions. These are the finite dimensional indecomposable rational linear representations of the additive group $\Ga$ of a field of characteristic zero, and…

Let X be a locally compact geodesically complete CAT(0) space and G be a discrete group acting properly and cocompactly on X. We show that G contains an element acting as a hyperbolic isometry on each indecomposable de Rham factor of X. It…

Let G/K be a non-compact, rank-one, Riemannian symmetric space and let G^C be the universal complexification of G. We prove that a holomorphically separable, G-equivariant Riemann domain over G^C / K^C is necessarily univalent, provided…

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…

Let $M$ be a compact connected pseudo-Riemannian manifold on which a solvable connected Lie group $G$ of isometries acts transitively. We show that $G$ acts almost freely on $M$ and that the metric on $M$ is induced by a bi-invariant…

Let $G$ be a totally disconnected, locally compact group and let $H$ be an equicontinuously (for example, compactly) generated group of automorphisms of $G$. We show that every distal action of $H$ on a coset space of $G$ is a SIN action,…

Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques do not directly apply. We show that, when a group $G$ acts…

The main goal of this paper is to obtain a formula for the T-equivariant Riemann-Roch number of certain G-spaces which are the finite dimensional models of certain infinite dimensional spaces with Hamiltonian LG-actions, here T is a maximal…

If $G$ is a group acting on a tree $X$, and ${\mathcal S}$ is a $G$-equivariant sheaf of vector spaces on $X$, then its compactly-supported cohomology is a representation of $G$. Under a finiteness hypothesis, we prove that if $H_c^0(X,…

The object of this paper is to prove some general results about rational idempotents for a finite group $G$ and deduce from them geometric information about the components that appear in the decomposition of the Jacobian variety of a curve…

Let $(Z,\omega)$ be a \Keler manifold and let $U$ be a compact connected Lie group with Lie algebra $\mathfrak{u}$ acting on $Z$ and preserving $\omega$. We assume that the $U$-action extends holomorphically to an action of the complexified…

For a discrete metric space (or more generally a large scale space) $X$ and an action of a group $G$ on $X$ by coarse equivalences, we define a type of coarse quotient space $X_G$, which agrees up to coarse equivalence with the orbit space…

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichm\"uller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

By an additive action on an algebraic variety $X$ we mean a regular effective action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the commutative unipotent group $\mathbb{G}_a^n$. In this paper, we give a classification of additive…