Related papers: The N=1 triplet vertex operator superalgebras
The $\mathbb{Z}/2\mathbb{Z}$--graded intertwining operators are introduced. We study these operators in the case of ``degenerate'' N=1 minimal models, with the central charge $c=3/2$. The corresponding fusion ring is isomorphic to the…
We introduce the notion of N=1 supergeometric vertex operator superalgebra motivated by the worldsheet geometry underlying genus-zero, two-dimensional, holomorphic N=1 superconformal field theory. We then show, assuming the convergence of…
We give an explicit construction of all complex continuous irreducible characters of the group ${\rm SL}_1(D)$, where $D$ is a division algebra of prime degree $\ell$ over a local field of odd residual characteristic different than $\ell$.…
In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules $L$ over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras $\mathfrak{g}$. The problems…
$W$-algebras are certain algebraic structures associated to a finite dimensional Lie algebra $\mathfrak g$ and a nilpotent element $f$ via Hamiltonian reduction. In this note we give a review of a recent approach to the study of (classical…
The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple…
We construct a family of right coideal subalgebras of quantum groups, which have the property that all irreducible representations are one-dimensional, and which are maximal with this property. The obvious examples for this are the standard…
We construct geometrically the generating fields of a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes of n points on a projective surface for all n. We compute explicitly the commutators…
We study quantum mechanical systems with $\mathfrak{osp}(4^{*}|4)$ superconformal symmetry. We classify unitary lowest-weight representations of this superconformal algebra and define an index which receives contributions from short and…
We classify the irreducible modules for the fixed point vertex operator subebra of the rank 1 free bosonic VOA under the -1 automorphism.
We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the…
In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…
We study the representation theory of the subregular W-algebra $\mathcal{W}^k(\mathfrak{so}_{2n+1},f_{sub})$ of type B and the principal W-superalgebra $\mathcal{W}^\ell(\mathfrak{osp}_{2|2n})$, which are related by an orthosymplectic…
We classify irreducible representations of finite $W$-algebra of the queer Lie superalgebra $Q(n)$ associated with the principal nilpotent coadjoint orbits. We use this classification and our previous results to obtain a classification of…
Let $\mathcal{O}^{int}_q(m|n)$ be a semisimple tensor category of modules over a quantum ortho-symplectic superalgebra of type $B, C, D$ introduced in the author's previous work. It is a natural counterpart of the category of finitely…
Coulomb branches of vacua are the most universal moduli spaces that arise in local unitary interacting 4d $\mathcal{N}=2$ superconformal field theories (SCFTs). In these theories, $1/2$-BPS primaries parameterize the Coulomb branches and…
In the present paper, a class of new simple modules over the $N=1$ Ramond algebra are constructed, which are induced from simple modules over some finite dimensional solvable Lie superalgebras. These new modules are simple restricted…
The notions of N=1 Neveu-Schwarz vertex operator superalgebra over a Grassmann algebra and with odd formal variables and of N=1 Neveu-Schwarz vertex operator superalgebra over a Grassmann algebra and without odd formal variables are…
In this paper we consider extensions of the super Virasoro algebra by one and two super primary fields. Using a non-explicitly covariant approach we compute all SW-algebras with one generator of dimension up to 7 in addition to the super…
In this paper we use the Hecke algebra of type $B$ to define a new algebra $\Sch$ which is an analogue of the q-Schur algebra. We construct Weyl modules for $\Sch$ and obtain, as factor modules, a family of irreducible $\Sch$-modules over…