Related papers: On conformally invariant differential operators
Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some initial base case. The fact that these constructions produce…
This paper completes the construction of arbitrary order conformally invariant differential operators in higher spin spaces. Jan Slov\'{a}k has classified all conformally invariant differential operators on locally conformally flat…
Rapid progress has been made recently on symmetry breaking operators for real reductive groups. Based on Program A-C for branching problems (T.Kobayashi [Progr.Math.2015]), we illustrate a scheme of the classification of (local and…
We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on non-covariant operator regularizations, interesting operators here are true tensor objects with classical…
We present a novel approach to the classification of conformally equivariant differential operators on spinors in the case of homogeneous conformal geometry. It is based on the classification of solutions for a vector-valued system of…
Two differential calculi are developped on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same quantum group that is extended to a…
We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…
We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
We introduce the notion of Ricci-corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. This enables us to simplify the explicit formulae for standard…
We give a complete classification of conformally covariant differential operators between the spaces of $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$. Moreover, we find explicit formul{\ae} for…
In this paper we discuss some general properties of viscoelastic models defined in terms of constitutive equations involving infinitely many derivatives (of integer and fractional order). In particular, we consider as a working example the…
Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the action of a simple Lie algebra g are…
We find a three-parameter family of ordinary differential systems in dimension six with affine Weyl group symmetry of type $D_4^{(2)}$. This is the second example which gave higher order Painlev\'e type systems of type $D_{4}^{(2)}$. We…
Path geometries provide a geometric encoding of systems of second order ODE, which serves as a model for the geometric theory of more general systems of ODE and for cone structures. They are an instance of the family of parabolic…
Classical invariant theory of a complex reflection group $W$ highlights three beautiful structures: -- the $W$-invariant polynomials constitute a polynomial algebra, over which -- the $W$-invariant differential forms with polynomial…
We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
Let W be the Weyl group of a crystallographic root system acting on the associated weight lattice by reflections. In the present notes we extend the notion of an exponent of the W-action introduced in [Baek-Neher-Zainoulline,…
We compute the superpotentials for known families of Koszul Artin-Schelter regular algebras of dimension four using Magma, and apply Schur-Weyl duality from representation theory to determine the relevant invariants. Through the Borel-Weil…