Related papers: Joint Invariants of Linear Symplectic Actions
Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask…
We study infinitesimal semi-simple extrinsic symmetric spaces and give a classification in the symplectic case.
In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants…
The main purpose of this paper is calculation of differential invariants which arise from prolonged actions of two Lie groups SL(2) and SL(3) on the $n$th jet space of $R^2$. It is necessary to calculate $n$th prolonged infenitesimal…
We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces. Our proof uses sheaves of groupoids of Hamiltonian…
We investigate symmetries of the scalar field theory with harmonic term on the Moyal space with euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on…
We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in…
The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating…
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for classical field theories with symmetries.
We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spectral curve, one defined a sequence of differential forms,…
For any Lie group $G$, we construct a $G$-equivariant analogue of symplectic capacities and give examples when $G = \mathbb{T}^k\times\mathbb{R}^{d-k}$, in which case the capacity is an invariant of integrable systems. Then we study the…
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
This is a series of 5 lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory…
We exhibit a natural Lie algebra structure on the graded space of cyclic coinvariants of a symplectic vector space.
We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…
Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…
We survey results about computational complexity of the word problem in groups, Dehn functions of groups and related problems.