Related papers: On a Certain Stratification of the Gauge Orbit Spa…

The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight lattices, are classified. Finite subsets of the…

The orbits in $\Gamma_{\infty}(3) \backslash \Gamma(3)$ are in bijection with sets of invariants satisfying certain relations. We explain how wedge product matrices give an alternative definition of the invariants of matrix orbits. This new…

We introduce an elementary way of constructing principal (Z_2)^m-bundles over compact smooth manifolds. In addition, we will define a general notion of locally standard (Z_2)^m-actions on closed manifolds for all m>0, and then give a…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…

Let $S$ be a closed surface of genus $g$ greater than zero. In the present paper we study the topological-dynamical action of the mapping class group on the $\Bbb T^n$-character variety giving necessary and sufficient conditions for…

Using the dependent coordinates, the local Lagrange-Poincar\'e equations and equations for the relative equilibria are obtained for a mechanical system with a symmetry describing the motion of two interacting scalar particles on a special…

In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space $E_n$ are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a…

The values of the $T$ and $U$ moduli are studied for those ${\bf Z}_N $ Coxeter orbifolds with the property that some of the twisted sectors have fixed planes for which the six-torus ${\bf T}^6 $ can not be decomposed into a direct sum…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…

We give an explicit formula for the holonomy of the orientation bundle of a family of real Cauchy-Riemann operators. A special case of this formula resolves the orientability question for spaces of maps from Riemann surfaces with Lagrangian…

We construct the Hilbert space costratification of $G=\mathrm{SU}(2)$-quantum gauge theory on a finite spatial lattice in the Hamiltonian approach. We build on previous work where we have implemented the classical gauge orbit strata on…

For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in…

We determine the number of distinct fibre homotopy types for the gauge groups of principal $Sp(2)$-bundles over a closed, simply-connected four-manifold.

We consider generalized (possibly depending on fields as well as on space-time variables) gauge transformations and gauge symmetries in the context of general -- that is, possibly non variational nor covariant -- differential equations. In…

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on $SU_q(2)$ . The…

We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with…

Let $C\to M$ be the bundle of connections of a principal bundle on $M$. The solutions to Hamilton-Cartan equations for a gauge-invariant Lagrangian density $\Lambda $ on $C$ satisfying a weak condition of regularity, are shown to admit an…

Let $G$ be a non-compact simple Lie group with Lie algebra $\mathfrak{g}$. Denote with $m(\mathfrak{g})$ the dimension of the smallest non-trivial $\mathfrak{g}$-module with an invariant non-degenerate symmetric bilinear form. For an…

We consider a variant of the Seiberg-Witten equations for multiple-spinors. The moduli space of solutions to our generalized Seiberg-Witten equations in the setting of K\"ahler surfaces has a direct relation with ASD connections of…

For a topological group $G$ let $E_{\textsf{com}}(G)$ be the total space of the universal transitionally commutative principal $G$-bundle as defined by Adem--Cohen--Torres-Giese. So far this space has been most studied in the case of…