Related papers: Virtualization map for the Littelmann path model

We prove a Hitchin-Kobayashi correspondence for affine vortices generalizing a result of Jaffe-Taubes for the action of the circle on the affine line. Namely, suppose a compact Lie group K has a Hamiltonian action on a Kaehler manifold X…

The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one correspondences between the set of highest paths and the set of rigged configurations. In this paper, we give a crystal theoretic reformulation of the KKR map from the paths…

Abramovich, Corti and Vistoli have studied modular compactifications of stacks of curves equipped with abelian level structures arising as substacks of the stack of twisted stable maps into the classifying stack of a finite group, provided…

We construct a one-to-one correspondence between the Verma basis vectors of a finite dimensional irreducible representation $L(\lambda)$ of the symplectic Lie algebra $\mathfrak{sp}_4$ and the Kashiwara-Nakashima tableaux of…

Given a group endowed with a Z/2-valued morphism we associate a Gauss diagram theory, and show that for a particular choice of the group these diagrams encode faithfully virtual knots on a given arbitrary surface. This theory contains all…

We prove that for every finitely generated subgroup of a virtually connected Lie group which admits a finite dimensional model for the classifying space for proper actions the assembly map in algebraic K-theory is split injective. We also…

We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featuring a Willmore-type curvature penalization. The effective…

In addition to extending some facts from field coefficients to commutative ring coefficients for Leavitt path algebras with new shorter proofs, we also prove some results that are new even for field coefficients. In particular, we show that…

In this article, an alternative interpretation of the Seiberg-Witten map in non-commutative field theory is provided. We show that the Seiberg-Witten map can be induced in a geometric way, by a field dependent co-ordinate transformation…

In this paper, we prove the Lipschitz regularity of continuous harmonic maps from an finite dimensional Alexandrov space to a compact smooth Riemannian manifold. This solves a conjecture of F. H. Lin in \cite{lin97}. The proof extends the…

We show how the Hamiltonian lattice loop representation can be cast straightforwardly in the path integral formalism. The procedure is general for any gauge theory. Here we present in detail the simplest case: pure compact QED. We also…

In this article, we study the variation of the Gieseker and Uhlenbeck compactifications of the moduli spaces of Mumford-Takemoto stable vector bundles of rank 2 by changing polarizations. Some {\it canonical} rational morphisms among the…

Persistent homology maps a simplicial complex filtered by elements in $\mathbb R$ to finite formal sums of elements of $\mathbb R_{\leq}^{2} = \{ (b,d) \in \mathbb R^2 \cup \{ \infty \} \mid b < d \}$ called (finite) persistence diagrams.…

We give a new combinatorial model for the crystals of integrable highest weight modules over the classical Lie algebras of type $B$ and $C$ in terms of classical Young tableux. We then obtain a new description of its Littlewood-Richardson…

Recently, Hoshina, Fujii, and Kikukawa pointed out that the naive lattice gauge theory action in Minkowski signature does not result in a unitary theory in the continuum limit, and Kanwar and Wagman proposed alternative lattice actions to…

For a weighted graph $E$, we construct representation graphs $F$, and consequently, $L_K(E)$-modules $V_F$, where $L_K(E)$ is the Leavitt path algebra associated to $E$, with coefficients in a field $K$. We characterise representation…

We present an invariant relational path-integral quantization framework for general-relativistic gauge field theories based on the Dressing Field Method. The construction implements an automatic anomaly-cancellation mechanism that…

Using a distributed representation formula of the Gateaux derivative of the Dirichlet to Neumann map with respect to movements of a polygonal conductivity inclusion, [11], we extend the results obtained in [8] proving global Lipschitz…

We define a diagram associated to any algebraic connection on a vector bundle on a Zariski open subset of the Riemann sphere, extending the definition of Boalch-Yamakawa to the general case featuring several irregular singularities,…

We construct a new compactification of the moduli space of maps from pointed nonsingular projective stable curves to a nonsingular projective variety with prescribed ramification indices at the points. It is shown to be a proper…