Related papers: Deformations and Inversion Formulas For Formal Aut…
This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic…
Starting from integrable $su(2)$ (quasi-)spin Richardson-Gaudin XXZ models we derive several properties of integrable spin models coupled to a bosonic mode. We focus on the Dicke-Jaynes-Cummings-Gaudin models and the two-channel…
We generalize the notion of the auto-Igusa zeta function to formal deformations of algebraic spaces. By incorporating data from all algebraic transformations of local coordinates, this function can be viewed as a generalization of the…
We show that in the single component situation all perturbation variables in the comoving gauge are conformally invariant to all perturbation orders. Generally we identify a special time slicing, the uniform-conformal transformation…
We introduce a new set of noncommutative space-time commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative space-time relations taken here to have position…
We derive a functional It\^o-formula for non-anticipative maps of rough paths, based on the approximation properties of the signature of c\`adl\`ag rough paths. This result is a functional extension of the It\^o-formula for c\`adl\`ag rough…
In this paper we study high order expansions of chart maps for local finite dimensional unstable manifolds of hyperbolic equilibrium solutions of scalar parabolic partial differential equations. Our approach is based on studying an…
We propose a new procedure to embed second class systems by introducing Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be…
We provide and discuss complex analytic methods for overcoming the formal character of formal deformation quantization. This is a necessity for returning to physically meaningful statements, and accounts for the fact that the formal…
Unfolding singular points in linear differential equations is a classical technique for studying the properties of irregular singularities by relating them to regular singularities. In this paper, we propose a general framework for…
We study the decomposition of free random variables in terms of their orthogonal replicas from a new perspective. First, we show that the mixed moments of orthogonal replicas with respect to the normalized linear functional $\Phi$ are…
We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation depends on a short-distance scale \ell_p, and thus breaks scale invariance, but preserves all space-time isometries. The…
We introduce the notion of $k$-regular factorizations for contractions into $k$ factors, generalizing the classical notion of regular factorization due to Sz.-Nagy and Foia\c{s}, and develop a systematic framework for their analysis. Using…
Non-linear electrodynamics arising in the frames of field theories in non-commutative space-time is examined on the base of the Riemann-Silberstein-Majorana-Oppenheimer formalism. The problem of form-invariance of the non-linear…
We study the displacement map associated to small one-parameter polynomial unfoldings of polynomial Hamiltonian vector fields on the plane. Its leading term, the generating function $M(t)$, has an analytic continuation in the complex plane…
In this note, we establish a relationship between fractional Dehn twist coefficients of Riemann surface automorphisms and modular invariants of holomorphic families of algebraic curves. Specially, we give a characterization of…
Let k denote a perfect field of characteristic 5. We show that the versal deformation ring of an element of order 5 and Hasse conductor 2 as automorphism of a ring of formal power series k[[t]] computed by Bertin and Mezard, is in fact…
In the context of rational conformal field theories (RCFT) we look into the problem of constructing and classifying pairs consisting of a local operator and a topological defect which commutes or anticommutes with it. We discuss the bulk…
Local Scale-Invariance theory is tested by extensive dynamical simulations of the driven dimer lattice gas model, describing the surface growth of the 2+1 dimensional Kardar-Parisi-Zhang surfaces. Very precise measurements of the universal…
We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting…