Related papers: W_{N+1}-constraints for singularities of type A_N
We show that for polytopes P_1, P_2, ..., P_r \subset \R^d, each having n_i \ge d+1 vertices, the Minkowski sum P_1 + P_2 + ... + P_r cannot achieve the maximum of \prod_i n_i vertices if r \ge d. This complements a recent result of Fukuda…
A Dirichlet operator algebra is a nonself-adjoint operator algebra $\mathcal{A}$ with the property that $\mathcal{A} + \mathcal{A}^*$ is norm-dense in the C$^*$-envelope of $\mathcal{A}.$ We show that, under certain restrictions,…
In this paper, we revisit scalar field theories in $d$ space-time dimensions possessing $U(N)$ global symmetry. Following our recent work arXiv:1402.1430v2, we consider the generating function of correlation functions of all…
This paper investigates a multilayered Helmholtz model in $\mathbb{R}^d$ ($d \ge 2$) characterized by concentric layers of materials with alternating positive and negative refractive indices. To overcome the loss of coercivity induced by…
We study a new class of infinite-dimensional Lie algebras W_\infty(p,q) generalizing the standard W_\infty algebra, viewed as a tensor operator algebra of SU(1,1) in a group-theoretic framework. Here we interpret W_\infty(p,q) either as an…
By imposing the weighted renormalization condition and the (super)symmetry requirements, we construct a Lifshitz-like extension of the three-dimensional Wess-Zumino model, with dynamical critical exponent z=2. In this context, the auxiliary…
We explore a class of CFT's with higher spin currents and charges. Away from the free or $N=\infty$ limit the non-conservation of currents is governed by operators built out of the currents themselves, which deforms the algebra of charges…
In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$,…
For an irreducible complex reflection group $W$ of rank $n$ containing $N$ reflections, we put $g=2N/n$ and construct a $(g+1)^n$-dimensional irreducible representation of the Cherednik algebra which is (as a vector space) a quotient of the…
We integrate the Lifting cocycles $\Psi_{2n+1},\Psi_{2n+3},\Psi_{2n+5},...$ ([Sh1], [Sh2]) on the Lie algebra $\Dif_n$ of holomorphic differential operators on an $n$-dimensional complex vector space to the cocycles on the Lie algebra of…
We study conical defect geometries in the SL(N) Chern-Simons formulation of higher spin gauge theories in AdS_3. We argue that (for N\geq 4) there are special values of the deficit angle for which these geometries are actually smooth…
Consider the eigenvalue problem generated by a fixed differential operator with a sign-changing weight on the eigenvalue term. We prove that as the negative part of the weight is rescaled towards negative infinity on some subregion, the…
The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in $n$ dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the…
In this paper, we begin the study of highest weight representations of the quantized enveloping superalgebra ${\mathfrak U}_q {\mathfrak p}_n$ of type $P$. We introduce a Drinfeld-Jimbo representation and establish a…
It is shown that an elliptic scattering operator $A$ on a compact manifold with boundary with coefficients in the bounded operators of a bundle of Banach spaces of class (HT) and Pisier's property $(\alpha)$ has maximal regularity (up to a…
Consider the maximal nilpotent subalgebra $n_+(A_1^{(1)})$ of the simplest affine algebra $A_1^{(1)}$ which is one of the $\mathbb{N}$-graded Lie algebras with minimal number of generators. We show truncated versions of this algebra in…
In this paper we study unitary Ramond twisted representations of minimal $W$-algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal highest weight (unitarity in the Ramond extremal case, as well…
What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet completion must be string theory. We provide more…
Let $n\ge 2$ be a positive integer. To each irreducible representation $\sigma$ of $\mathrm{Sp}(1)$, an $\mathrm{Sp}(1)$-Kepler problem in dimension $(4n-3)$ is constructed and analyzed. This system is super integrable and when $n=2$ it is…
We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the role of the (Lorentzian) modulus of its differential. It is…