Related papers: Constructions of $SU(2)$ and Weyl equivariant maps…

We study the duality group of $\hat{A}_{n-1}$ quiver gauge theories, primarily using their M5-brane construction. For $\mathcal{N}=2$ supersymmetry, this duality group was first noted by Witten to be the mapping class group of a torus with…

Motivated by the simplicity and direct phenomenological applicability of field-theoretic orbifold constructions in the context of grand unification, we set out to survey the immensely rich group-theoretical possibilities open to this type…

We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…

Let $p$ be an odd prime. For a compact Lie group $G$ and an elementary abelian $p$-group $A$ of $G$, one may define the Weyl group $W_A$ of $A$ in a similar fashion as defining the Weyl group of a maximal torus, such that $W_A$ acts on…

The present article investigates Sp(3) structures on 14-dimensional Riemannian manifolds, a continuation of the recent study of manifolds modeled on rank two symmetric spaces (here: SU(6)/Sp(3)). We derive topological criteria for the…

This is a footnote to earlier joint work with Yu. Berest, which constructed a bijection between the space of ideal classes of the Weyl algebra and a union of Calogero-Moser varieties. A key property of this bijection is that it is…

We explain how to apply techniques from integrable systems to construct $2k$-soliton homoclinic wave maps from the periodic Minkowski space $S^1\times R^1$ to a compact Lie group, and more generally to a compact symmetric space. We give a…

Let $W$ be the Weyl group of a split semisimple group $G$. Its Hecke category $\mathsf{H}_W$ can be built from pure perverse sheaves on the double flag variety of $G$. By developing a formalism of generalized realization functors, we…

Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $\theta$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_\theta(G) \subseteq V$ of semistable points. We give necessary,…

Let $\omega_\mathfrak{g}$ be a Lie algebra valued differential $1$-form on a manifold $M$ satisfying the structure equations $d \omega_\mathfrak{g} + \frac{1}{2} \omega_\mathfrak{g}\wedge \omega_\mathfrak{g}=0$ where $\mathfrak{g}$ is…

Seiberg-Witten maps are a well-established method to locally construct noncommutative gauge theories starting from commutative gauge theories. We revisit and classify the ambiguities and the freedom in the definition. Geometrically,…

In this paper we consider the re-expansion problems on compact Lie groups. First, we establish weighted versions of classical re-expansion results in the setting of multi-dimensional tori. A natural extension of the classical re-expansion…

Let $G$ be a finite group of Lie type $E_6$ over $F_q$ (adjoint or simply connected) and $W$ be the Weyl group of $G$. We describe maximal tori $T$ such that $T$ has a complement in its algebraic normalizer $N(G,T)$. It is well known that…

A theorem of Cantat and Urech says that an analog of the classical Tits alternative holds for the group of birational automorphisms of a compact complex Kaehler surface. We established in our previous paper the following Tits-type…

Let $G$ be a connected semi-simple group defined over and algebraically closed field, $T$ a fixed Cartan, $B$ a fixed Borel containing $T$, $S$ a set of simple reflections associated to the simple positive roots corresponding to $(T,B)$,…

Boij-S\"oderberg theory characterizes syzygies of graded modules and sheaves on projective space. This paper continues earlier work with S. Sam, extending the theory to the setting of $GL_k$-equivariant modules and sheaves on Grassmannians.…

A new universal model to implement the Seiberg-Witten approach to low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It is based on the…

Let $G, H$ be two Kleinian groups with homeomorphic quotients $\mathbb H^3/G$ and $\mathbb H^3/H$. We assume that $G$ is of divergence type, and consider the Patterson-Sullivan measures of $G$ and $H$. The measurable rigidity theorem by…

It is a Theorem of W.~ W. Comfort and K.~ A. Ross that if $G$ is a subgroup of a compact Abelian group, and $S$ denotes those continuous homomorphisms from $G$ to the one-dimensional torus, then the topology on $G$ is the initial topology…

For a compact Lie group $G$ with maximal torus $T$, Pittie and Smith showed that the flag variety $G/T$ is always a stably framed boundary. We generalize this to the category of $p$-compact groups, where the geometric argument is replaced…