相关论文: Singular vectors of $N=1$ super Virasoro algebra v…

It was conjectured in arXiv:1211.2788 that bosonization of singular vectors (in Neveu-Schwarz sector) of $\mathcal{N}=1$ super analog of the Virasoro algebra can be identified with Uglov symmetric function. In the paper we prove this…

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…

We calculate explicitly the singular vectors of the Virasoro algebra with the central charge $c\leq 1$. As a result, we have an infinite sequence of the singular vectors for each Fock space with given central charge and highest weight, and…

A general construction is found for `topological' singular vectors of the twisted N=2 superconformal algebra. It demonstrates many parallels with the known construction for sl(2) singular vectors due to Malikov--Feigin--Fuchs, but is…

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…

Bauer, Di Francesco, Itzykson and Zuber proposed recently an algorithm to construct all singular vectors of the Virasoro algebra. It is based on the decoupling of (already known) singular fields in the fusion process. We show how to extend…

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…

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…

We give explicit formulae of Whittaker vectors for Virasoro algebra in terms of the Jack symmetric polynomials. Our fundamental tools are the Feigin-Fuchs bosonization and the split expression of the Calogero-Sutherland model given by…

We propose to parametrize the configuration space of one-dimensional quantum systems of N identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the…

A recent novel derivation of the representation of Virasoro singular vectors in terms of Jack polynomials is extended to the supersymmetric case. The resulting expression of a generic super-Virasoro singular vector is given in terms of a…

A depending on a complex parameter $k$ superanalog ${\mathcal S}{\mathcal L}$ of Calogero operator is constructed; it is related with the root system of the Lie superalgebra ${\mathfrak{gl}}(n|m)$. For $m=0$ we obtain the usual Calogero…

We consider the linearization of $N = 1$ nonlinear supersymmetry (NLSUSY) based on a commutator algebra in Volkov-Akulov NLSUSY theory. We show explicitly that $U(1)$ gauge and scalar supermultiplets in addition to a vector supermultiplet…

We present subsingular vectors of the N=2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the…

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…

Using explicit expressions for a class of singular vectors of the $N=2$ (untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and Kent, we show that the analytically extended Verma modules contain two linearly independent…

According to Kirillov's theory, the construction of a unitary irreducible representation of a nilpotent Lie group requires a precise computation of some polarizing subalgebra subordinated to a linear functional in the linear dual of the…

New superconformal extensions of d=1 Calogero-type systems are obtained by gauging the U(n) isometry of matrix superfield models. We consider the cases of N=1, N=2 and N=4 one-dimensional supersymmetries. The bosonic core of the N=1 and N=2…

The BRST quantisation of the Drinfeld - Sokolov reduction applied to the case of $A^{(1)}_2\,$ is explored to construct in an unified and systematic way the general singular vectors in ${\cal W}_3$ and ${\cal W}_3^{(2)}$ Verma modules. The…

We investigate extensions of the N=2 super Virasoro algebra by one additional super primary field and its charge conjugate. Using a supersymmetric covariant formalism we construct all N=2 super W-algebras up to spin 5/2 of the additional…