相关论文: Singular vectors for the $W_N$ algebras

We present a general vertex operator construction based on the Fock space for an affine Lie algebras of type $A$. This construction allows us to give a unified treatment for both the homogeneous and principle realizations of the affine Lie…

J.~Lepowsky and R.~L.~Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via vertex operator constructions of standard (i.e. integrable highest weight) representations of affine Kac-Moody Lie algebras.…

We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness…

We introduce a code construction for Wess-Zumino-Witten (WZW) models associated with simply-laced affine Lie algebras at level 1. The chiral primary fields of these rational CFTs can be parametrized by the elements of the outer automorphism…

We provide the first formulae for the weights of all simple highest weight modules over Kac-Moody algebras. For generic highest weights, we present a formula for the weights of simple modules similar to the Weyl-Kac character formula. For…

We study the monoid of so called projection functors $\p{S}$ attached to simple modules $S$ of a finite dimensional algebra, which appear naturally in the study of torsion pairs. We determine defining relations in special cases of path…

We construct a monomorphism of the De Rham complex of scalar multivalued meromorphic forms on the projective line, holomorphic on the complement to a finite set of points, to the chain complex of the Lie algebra of $sl_2$-valued algebraic…

In this paper we first prove that the maximal ideal of the universal affine vertex operator algebra $V^k(sl_n)$ for $k=-n+\frac{n-1}{q}$ is generated by two singular vectors of conformal weight $3q$ if $n=3$, and by one singular vector of…

The Kac determinant for the Topological N=2 superconformal algebra is presented as well as a detailed analysis of the singular vectors detected by the roots of the determinants. In addition we identify the standard Verma modules containing…

Simple, or Kleinian, singularities are classified by Dynkin diagrams of type ADE. Let g be the corresponding finite-dimensional Lie algebra, and W its Weyl group. The set of g-invariants in the basic representation of the affine Kac-Moody…

Let $W$ be the Weyl group of a split semisimple group $G$. Its Hecke category $\mathsf{H}_W$ can be built from pure perverse sheaves on the double flag variety of $G$. By developing a formalism of generalized realization functors, we…

We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules…

We give a new construction of functors from the category of modules for the associative algebras $A_n(V)$ and $A_g(V)$ associated with a vertex operator algebra $V$, defined by Dong, Li and Mason, to the category of admissible $V$-modules…

We construct a vertex operator realization for the simple current primary fields of WZW theories which are based on simply laced affine Lie algebras g. This is achieved by employing an embedding of the integrable highest weight modules of g…

Let k be an algebraically closed field of arbitrary characteristic. First we give explicit bases for the highest weight vectors for the action of GL_r x GL_s on the coordinate ring k[Mat_{rs}^m] of m-tuples of r x s-matrices. It turns out…

This paper characterizes geometrically the singularities of limited DOF parallel manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vector of lines (finite and infinite) constituting the rows of the…

In this paper we examine an inverse problem in the modular theory of von Neumann algebras in the case of finite factors. First we give a characterization of cyclic and separating vectors for finite factors in terms of operators associated…

With this paper we start the study of reducible representations of the Jacobi algebra with the ultimate goal of constructing differential operators invariant w.r.t. the Jacobi algebra. In this first paper we show examples of the low level…

Let $\mathscr{C}$ be the category of finite dimensional modules over the quantum affine algebra $U_q(\widehat{\mathfrak{g}})$ of a simple complex Lie algebra ${\mathfrak{g}}$. Let $\mathscr{C}^-$ be the subcategory introduced by Hernandez…

We construct Wakimoto modules for twisted affine Lie algebras, and interpret the construction in terms of vertex algebras and their twisted modules. Using the Wakimoto realization, we prove the Kac-Kazhdan conjecture on the characters of…