相关论文: Null vectors of the W_3 algebra

Using the fusion principle of Bauer et al. we give explicit expressions for some null vectors in the highest weight representations of the \bc algebra in two different forms. These null vectors are the generalization of the Virasoro ones…

The null vectors of an arbitrary highest weight representation of the $WA_2$ algebra are constructed. Using an extension of the enveloping algebra by allowing complex powers of one of the generators, analysed by Kent for the Virasoro…

We use an argument of Romans showing that every Virasoro construction leads to realizations of $W_3$, to construct $W_3$ realizations on arbitrary affine Lie algebras. Solutions are presented for generic values of the level as well as for…

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…

It is shown that the ternary Virasoro-Witt algebra of Curtright, Fairlie and Zachos can be constructed by applying the Nambu commutator to the vect(1) realization on scalar densities. This construction is generalized to vect(d), but the…

We present two explicit expressions for generic singular vectors of type $(r,s)$ of the Virasoro algebra. These results follow from the paper of Bauer et al which presented recursive methods to construct the vectors. The expressions…

We derive a set of recursion formulae to construct singular vectors for the $N=2$ (untwisted) algebra, by using the approach of Bauer, di Francesco, Itzykson and Zuber. Applying these formulae, we obtain explicit expressions for the charged…

For vertex operator algebra V_{\sqrt{2}A_l} associated to the even lattice \sqrt{2}A_l which is \sqrt{2} times root lattice of type A_l, it was shown by Dong-Li-Maosn-Norton that the Virasoro vector is a sum of l+1 mutually orthogonal…

A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various…

We find necessary and sufficient conditions of irreducibility of vacuum modules over affine Lie algebras and superalgebras. From this we derive conditions of simplicity of minimal W-algebras. Moreover, in the case of Virasoro and…

Galilean $W_3$ vertex operator algebra $\mathcal GW_3(c_L,c_M)$ is constructed as a universal enveloping vertex algebra of certain non-linear Lie conformal algebra. It is proved that this algebra is simple by using determinant formula of…

Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as $W$-algebras. Known examples include contractions of pairs of the Virasoro algebra, its $N=1$…

We give a proof of the recursive formula on the norm of Whittaker vector of the deformed Virasoro algebra, which is an analog of the one for the Virasoro Lie algebra proposed by Al. Zamolodchikov. Our formula gives a proof of the pure SU(2)…

In this paper, a continuation of \cite{MPS}, we investigate the $S_3$-orbifold subalgebra of $(\mathcal{V}_c)^{\otimes 3}$, that is, we consider the $S_3$-fixed point vertex subalgebra of the tensor product of three copies of the universal…

Traces of powers of the zero mode in the W3 Algebra have recently been found to be of interest, for example in relation to Black Hole thermodynamics, and arise as the terms in an expansion of the full characters of the algebra. We calculate…

We obtain complete classification of in-equivalent realizations of the Virasoro algebra by Lie vector fields over the three-dimensional field of real numbers. As an application we construct new classes of nonlinear second-order partial…

We represent Feigin's construction [11] of lattice W algebras and give some simple results: lattice Virasoro and $W_3$ algebras. For simplest case $g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We find simplest…

We consider the nonlinear algebras $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ and find their realizations in terms of currents spanning conformal linearizing algebras. The specific structure of these algebras, allows us to construct…

We give expressions for the singular vectors in the highest weight representations of the Virasoro algebra. We verify that the expressions --- which take the form of a product of operators applied to the highest weight vector --- do indeed…

This paper studies restricted modules of gap-$p$ Virasoro algebra $\L$ and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted $\L$-modules of level…