Related papers: Hitchin Pairs for non-compact real Lie groups

We study the deformation of the holomorphic-Higgs pair. The holomorphic-Higgs pair is a pair of a complex manifold and a Higgs bundle over it. We introduce the differential graded Lie algebra (DGLA) which comes from the deformation. We…

Let $X$ be a compact connected K\"ahler manifold equipped with an anti-holomorphic involution which is compatible with the K\"ahler structure. Let $G$ be a connected complex reductive affine algebraic group equipped with a real form…

Through the action of anti-holomorphic involutions on a compact Riemann surface, we construct families of (A,B,A)-branes in the moduli spaces of G_c-Higgs bundles on the Riemann surface. We study the geometry of these (A,B,A)-branes in…

We provide a geometric construction of the unitary structure which is projectively preserved by the Hitchin connection. We analyze the asymptotic behavior of it and we establish that it is uniformly in the level equivalent to the Hermitian…

The purpose of this note is to give a simple proof of the fact that a certain substack, defined in [2], of the moduli stack $T^{\ast}Bun_G(\Sigma)$ of Higgs bundles over a curve $\Sigma$, for a connected, simply connected semisimple group…

We study the limiting behavior of the solutions $h_t$ of the Hitchin's equation associated with a family of stable SU(1,2) Higgs bundles $(L,F,t\beta,t\gamma)$ on a compact connected Riemann surface $X$ as $t\to\infty$ under the assumption…

We study orbits and reachable sets of generic couples of Hamiltonians $H_1, H_2$ on a symplectic manifold $N$. We prove that, $C^k$-generically for $k$ large enough, orbits coincide with the whole of $N$, and that the same is true for…

We initiate and develop the theory of complex harmonic maps to holomorphic Riemannian symmetric spaces, which we make use of to study complex analytic aspects of higher Teichm\"uller theory, with a focus on rank $2$ Hitchin components.…

Let $\varphi\colon X\rightarrow Y$ be a degree two Galois cover of smooth curves over a local field $F$ of odd characteristic. Assuming that $Y$ has good reduction, we describe a semi-stability criterion for the curve $X$, using the data of…

We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group $N$, there is a one-to-one correspondence between the set of isomorphism classes of connected Lie…

The aim of this paper is to give an explicit expression for Hitchin's connection in the case of rank 2 bundles with trivial determinant over curves of genus 2. We recall the definition of this connection (which arose in Quantum Field…

We build compact moduli spaces of Grassmannian framed bundles over a Riemann surface, essentially replacing a group by its bi-invariant compactification. We do this both in the algebraic and symplectic settings, and prove a…

The Hitchin component is a connected component of the character variety of reductive group homomorphisms from the fundamental group of a closed surface S of genus greater than 1 to the Lie group PSL_m(R). The Teichmuller space of S…

Let $M$ be a closed orientable Riemannian surface. Consider an SO(3)-connection $A$ and a Higgs field $\Phi:M\to so(3)$. The pair $(A,\Phi)$ naturally induces a cocycle over the geodesic flow of $M$. We classify (up to gauge…

Let $G$ be a split real form of a complex simple adjoint group whose Weyl group contains $-1$, let $\lambda$ be the Jordan projection of $G$, and let $S$ be a closed orientable surface of genus at least 2. For a $G$-Hitchin representation…

An effective family of spectral curves appearing in Hitchin fibrations is determined. Using this family the moduli spaces of stable Higgs bundles on an algebraic curve are embedded into the Sato Grassmannian. We show that the Hitchin…

The existence and uniqueness of H-N reduction for the Higgs principal bundles over nonsingular projective variety is shown. We also extend the notion of H-N reduction for (\Gamma, G)-bundles and ramified G-bundles over a smooth curve.

We study Hamiltonian field theories on the multisymplectic bundle of a principal G-bundle with Hamiltonian densities invariant under a subgroup $H\subset G$. Using the covariant bracket formulation, we reduce the polysymplectic space and…

Classic work of Pierce and Dauns-Hofmann shows that biregular rings are dual to simple ring bundles over Stone spaces. We extend this duality to Steinberg rings, a purely algebraic generalisation of Steinberg algebras, and ringoid bundles…

The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and…