Related papers: Relative symplectic Steinberg group
V.I. Kopeiko proved that over a euclidean ring, the symplectic group defined with respect to the standard skew-symmetric matrix is same as the elementary symplectic group. Here we generalise the result of Kopeiko for a symplectic group…
We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments.
We obtain the symplectic group $\SP(V)$ as the universal completion of an amalgam of low rank subgroups akin to Levi components. We let $\SP(V)$ act flag-transitively on the geometry of maximal rank subspaces of $V$. We show that this…
We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.
We classify bireflectional elements (products of 2 involutions) in symplectic groups Sp$(2n, K)$ over a field $K$. We also classify rev ersible elements (elements conjugate to their inverses) and bireflectional elements in finite projective…
We find an explicit presentation of relative odd unitary Steinberg groups constructed by odd form rings and of relative doubly laced Steinberg groups over commutative rings, i.e. the Steinberg groups associated with the Chevalley group…
These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…
We discuss symplectic and hyperk\"ahler implosion and present candidates for the symplectic duals of the universal hyperk\"ahler implosion for various groups.
We give a sufficient condition on a pair of (primitive) integral polynomials that the associated hypergeometric group (monodromy group of the corresponding hypergeometric differential equation) is an arithmetic subgroup of the integral…
We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.
In this note we prove that every finitely presented subgroup of a systolic group is itself systolic.
We show that right-angled Coxeter groups are relatively hyperbolic in the sense defined by Farb, relative to a natural collection of rank-2 parabolic subgroups.
We describe the structure of the Lie groups endowed with a left-invariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This…
We discuss some examples in which symplectic monodromy (provably or conjecturally) splits off the symplectic mapping class group, hoping to illustrate different techniques and inputs to the arguments. Along the way we formulate several open…
We derive a symplectic analogue of A-directed immersion theorem.
We present a simple remark that assures that the invariant theory of certain real Lie groups coincides with that of the underlying affine, real algebraic groups. In particular, this result applies to the non-compact orthogonal or symplectic…
I study flux groups of compact symplectic manifolds. Under some topological assumptions, I give a new estimate of the rank of flux groups and give a method of construcion of compact symplectic aspherical manifolds.
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.
We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also…