Related papers: Odd magical triples and maximal Higgs bundles

We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs bundles over a compact Riemann surface $\Sigma$ and consider a natural involution, studying its fixed point locus when $\Sigma$ is $\mathbb{C} \mathbb{P}^1$ and…

In this paper, we show that for any reductive group $G$ the moduli space of semistable $G$-Higgs bundles on a curve in characteristic $p$ is a twisted form of the moduli space of semistable flat $G$-connections. This is the semistable…

Let $X$ be an arbitrary non-compact hyperbolic Riemann surface, that is, not $\mathbb C$ or $\mathbb C^*$. Given a tuple of holomorphic differentials $\boldsymbol q=(q_2,\cdots,q_n)$ on $X$, one can define a Higgs bundle…

We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of dimensions on dual moduli spaces, answering…

Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed…

The central result of this paper is an identification of the shifted Cartier dual of the moduli stack $\mathcal{M}_{\mathfrak{g}}(C)$ of $\widetilde{G}$-Higgs bundles on $C$ of arbitrary degree (modulo shifts by $Z(\widetilde{G})$) with a…

We investigate the irreducibility of the nilpotent Slodowy slices that appear as the associated variety of W-algebras. Furthermore, we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves.

We find an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL(2) Higgs moduli space on a Riemann surface. On one side we have the components of the Lagrangian brane of U(1,1) Higgs…

Let $G$ be a simple and simply connected complex Lie group, ${\goth{g}}$ its Lie algebra. I remove the restriction ``$G$ is of classical type or $G_2$'' made on $G$ in the papers of Beauville, Laszlo and myself [L-S] and [B-L-S] on the…

In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called…

Let $k$ be an algebraic closure of a finite field of odd characteristic. We prove that for any rank two graded Higgs bundle with maximal Higgs field over a generic hyperbolic curve $X_1$ defined over $k$, there exists a lifting $X$ of the…

On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. The moduli spaces of these objects are…

The Hausel-Thaddeus conjectures concern topological mirror symmetry between moduli spaces of $SL_n$ and $PGL_n$ Higgs bundles on a curve. A non-archimedean approach was introduced by Groechenig, Wyss and Ziegler, proving the conjecture for…

We introduce a type of minimal surface in the pseudo-hyperbolic space $\mathbb{H}^{n,n}$ (with $n$ even) or $\mathbb{H}^{n+1,n-1}$ (with $n$ odd) associated to cyclic $\mathrm{SO}_0(n,n+1)$-Higg bundles. By establishing the infinitesimal…

We continue the study of Exceptional Periodicity and Magic Star algebras, which provide non-Lie, countably infinite chains of finite dimensional generalizations of exceptional Lie algebras. We analyze the graded algebraic structures arising…

Parabolic triples of the form $(E_*,\theta,\sigma)$ are considered, where $(E_*,\theta)$ is a parabolic Higgs bundle on a given compact Riemann surface $X$ with parabolic structure on a fixed divisor $S$, and $\sigma$ is a nonzero section…

Every $\mathbb{A}^{1}-$bundle over the complex affine plane punctured at the origin, is trivial in the differentiable category but there are infinitely many distinct isomorphy classes of algebraic bundles. Isomorphy types of total spaces of…

We carry an intrinsic approach to the study of the connectedness of the moduli space $\mathcal{M}_G$ of $G$-Higgs bundles, over a compact Riemann surface, when $G$ is a complex reductive (not necessarily connected) Lie group. We prove that…

This paper studies spaces of generalized theta functions for odd orthogonal bundles with nontrivial Stiefel-Whitney class and the associated space of twisted spin bundles. In particular, we prove a Verlinde type formula and a dimension…

Odd $K$-theory has the interesting property that it admits an infinite number of inequivalent differential refinements. In this paper we provide a bundle theoretic model for odd differential $K$-theory using the caloron correspondence and…