Related papers: Group invariant variational principles

We determine the rings of invariants in the symmetric algebra on the dual of a vector space V over the field of two elements, for the group G of orthogonal transformations preserving a non-singular quadratic form on V. The invariant ring is…

We give a short proof of a Grothendieck-Lefschetz Theorem for equivariant Picard groups of nonsingular varieties with the action of an affine algebraic group.

We present the method of group foliation for constructing non-invariant solutions of partial differential equations on an important example of the Boyer-Finley equation from the theory of gravitational instantons. We show that the…

This is the third paper of a series relating the equivariant twisted $K$-theory of a compact Lie group $G$ to the ``Verlinde space'' of isomorphism classes of projective lowest-weight representations of the loop groups. Here, we treat…

We prove a Grothendieck-Lefschetz theorem for equivariant Picard groups of non-singular varieties with finite group actions.

We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler--Poincar\'e equations defined on the Virasoro-Bott group, by using the inverse map (also called…

This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by…

In this paper we investigate the physical spectrum of the gravitational theory based on the Poincar\'e group with terms which are at most quadratic in tetrad and spin connection, allowing for the presence of parity-even as well as…

We give a new proof, inspired by an argument of Atiyah, Bott and Patodi, of the first fundamental theorem of invariant theory for the orthosymplectic super group. We treat in a similar way the case of the periplectic super group. Lastly,…

In this short note we give a proof of the refined version of the uniform invariant approximation property for compact (non-commutative) groups following the Bourgain's approach.

The Casselman-Wallach theorem is a foundational result in the theory of representations of real reductive groups connecting algebraic representations to topological representations. We provide a quantitative version of this theorem. For…

Our starting point is Mumford's conjecture, on representations of Chevalley groups over fields, as it is phrased in the preface of "Geometric Invariant Theory". After extending the conjecture appropriately, we show that it holds over an…

We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions,…

We present a notion of symmetry for 1+1-dimensional integrable systems which is consistent with their group theoretic description and reproduces in special cases the known Baecklund transformation for the generalized Korteweg-deVries…

We introduce a combinatorial property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a canonical finite presentation. We also define…

We review the construction and applications of exactly Poincar\'e invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar\'e group on few-particle Hilbert…

Consider the diagonal action of the special orthogonal group on the direct sum of a finite number of copies of the standard representation--the underlying field is assumed to be algebraically closed and of characteristic not equal to two.…

In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level.

In this article, we bring a new light on the concept of the inf-convolution operation $\oplus$ and provides additional informations to the work started in \cite{Ba1} and \cite{Ba2}. It is shown that any internal law of group metric…

In a previous paper we have introduced the gauge-equivariant K-theory group of a bundle endowed with a continuous action of a bundle of compact Lie groups. These groups are the natural range for the analytic index of a family of…