Related papers: Intertwining operator superalgebras and vertex ten…
A super-algebraic formulation of the N=2 supersymmetric unconstrained matrix (k|n,m)-MGNLS hierarchies (nlin.SI/0201026) is established. Recursion operators, fermionic and bosonic symmetries as well as their superalgebra are constructed for…
We construct integrated and unintegrated vertex operators for the type II superstring using the B-RNS-GSS formalism. The construction is done in flat spacetime background for both type II superstrings and type IIB superstring in a…
In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra.…
A list of superconformal chiral operator product expansion algebras with quadratic nonlinearity in two dimensions is completed on the basis of the known classification of little conformal Lie superalgebras. In addition to the previously…
We study superdifferential operators of order $2n+1$ which are covariant with respect to superconformal changes of coordinates on a compact super Riemann surface. We show that all such operators arise from super M\"obius covariant ones. A…
We present in this work a systematic study of integrable models and supersymmetric extensions of the Gelfand-Dickey algebra of pseudo differential operators. We describe in detail the relation existing between the algebra of super…
The infinite configuration space of an integrable vertex model based on $U_q\bigl(\hat{gl}(2|2)\bigr)_1$ is studied at $q=0$. Allowing four particular boundary conditions, the infinite configurations are mapped onto the semi-standard…
We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible $N=2$ supersymmetric integrable hierarchies with $N=2$ super $W_n$ second hamiltonian structure. We check this…
The traces over infinite dimensional representations of the central extended Yangian double for the product of operators which intertwine these representations are calculated. For the special combinations of the intertwining operators the…
The second part of our work on operator synthesis deals with individual operator synthesis of elements in some tensor products, in particular in Varopoulos algebras, and its connection with linear operator equations. Using a developed…
In this paper we study a series of vertex operator algebras of integer level associated to the affine Lie algebra $A_{\ell}^{(1)}$. These vertex operator algebras are constructed by using the explicit construction of certain singular…
We study the supersymmetric Gelfand-Dickey algebras associated with the superpseudodifferential operators of positive as well as negative leading order. We show that, upon the usual constraint, these algebras contain the N=2 super Virasoro…
Let V be a vertex operator algebra. We construct a sequence of associative algebras A_n(V) (n=0,1,2,...) such that A_{n}(V) is a quotient of A_{n+1}(V) and a pair of functors between the category of A_n(V)-modules which are not…
We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Conditions are given for the existence or nonexistence of coherent associative structures for such fusion rules,…
Following Beurling's theorem the natural compressions of the multiplication operator in the classical $L^2$ space are compressions to model spaces and to their orthogonal complements. Two possibly different model spaces are considered hence…
In this paper we introduce a variant of weight modules for certain conformal vertex superalgebras as an appropriate framework of the $\mathcal{N}=2$ supersymmetric coset construction. We call them weight-wise admissible modules. Motivated…
We prove a sharpened version of a conjecture of Dong-Mason about lattice subalgebras of a strongly regular vertex operator algebra $V$, and give some applications. These include the existence of a canonical conformal subVOA $W\otimes…
Let $V$ be a vertex operator superalgebra with the natural order 2 automorphism $\sigma$. Under suitable conditions on $V$, the $\sigma$-fixed subspace $V_{\bar 0}$ is a vertex operator algebra and the category $C_{V_{\bar 0}}$ of $V_{\bar…
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. This theory generalizes the tensor category theory for…
For a symmetric pair $(G,H)$ of reductive groups we construct a family of intertwining operators between spherical principal series representations of $G$ and $H$ that are induced from parabolic subgroups satisfying certain compatibility…