Related papers: NSR singular vectors from Uglov polynomials
We consider Borcherds superalgebras obtained from semisimple finite-dimensional Lie algebras by adding an odd null root to the simple roots. The additional Serre relations can be expressed in a covariant way. The spectrum of generators at…
We use recently derived explicit formulae for the Virasoro algebra's singular vectors to give constructive proofs of three results due to Feigin and Fuchs. The main result, which is needed for a rigorous treatment of fusion, describes the…
An algorithmic proof of the General N\'eron Desingularization theorem and its uniform version is given for morphisms with big smooth locus. This generalizes the results for the one-dimensional case.
We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…
We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric…
We display the construction of a twisted superalgebra for the N=1 Euclidian supergravity on 4-manifolds with an almost complex structure. It acts on a representation of twisted supersymmetry made of forms with odd and even statistics and it…
Let $(\mathfrak{g},\mathfrak{k})$ be a supersymmetric pair arising from a finite-dimensional, symmetrizable Kac-Moody superalgebra $\mathfrak{g}$. An important branching problem is to determine the finite-dimensional highest-weight…
Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This…
We consider the question of determining the structure of the set of all $d$-dimensional vectors of the form $N^{-1}(1_A*1_{-A}(x_1), ..., 1_A*1_{-A}(x_d))$ for $A \subseteq \{1,...,N\}$, and also the set of all $(2N+1)^{-1}(1_B*1_B(x_1),…
We present an explicit formula for a new family of Virasoro singular vectors. As a corrolary we get formulas for differentials of Feigin-Fuchs-Rocha-Carridi-Wallach resolution of the the positive nilpotent part of Virasoro (or Witt) algebra…
We construct a bosonization of the quantum superalgebra $U_q(\hat{sl}(N|1))$ for an arbitrary level $k$. We construct the screening that commutes with the quantum superalgebra for an arbitrary level $k \neq -N+1$. We propose a bosonization…
This work focuses on the study of monodromic singularities in planar analytic families of vector fields whose Newton diagram consists of exactly two edges. We begin by analyzing the desingularization scheme of a minimal model of polynomial…
We introduce a unital associative algebra ${\mathcal{SV}ir\!}_{q,k}$, having $q$ and $k$ as complex parameters, generated by the elements $K^\pm_m$ ($\pm m\geq 0$), $T_m$ ($m\in \mathbb{Z}$), and $G^\pm_m$ ($m\in \mathbb{Z}+{1\over 2}$ in…
A notion of duality of weight systems which corresponds to Batyrev's toric mirror symmetry is given. Explicit duality on the (1,1)-cohomology of K3 surfaces which are minimal models of toric hypersurfaces is constructed using monomial…
We study several families of vertex operator superalgebras from a jet (super)scheme point of view. We provide new examples of vertex algebras which are "chiralizations" of their Zhu's Poisson algebras $R_V$. Our examples come from affine…
We find and describe unexpected isomorphisms between two very different objects associated to hypersurface singularities. One object is the Milnor algebra of a function, while the other object associated to a singularity is the local ring…
The notion of "N = 2 vertex superalgebra with two odd formal variables" is presented, the main axiom being a Jacobi identity with odd formal variables in which an N=2 superconformal shift is incorporated into the usual Jacobi identity for a…
In this paper, we give a construction of simple modules generalizing and including both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We…
We initiate a systematic study of supersymmetric backgrounds in 4d $\mathcal{N}=2$ Euclidean supergravity in the presence of infinite towers of higher derivative corrections. Adopting a Gibbons-Hawking view towards the evaluation of the…
The single-trace, infinite-N algebra of an arbitrary region may or may not be a von Neumann algebra depending on the GNS sector. In this paper we identify the holographic dual of this mechanism as a consequence of the focusing of null…