Singular vectors of the WA2 algebra
نویسنده
چکیده
The null vectors of an arbitrary highest weight representation of the WA2 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 theory, we generate all the singular vectors indicated by the Kac determinant. We prove that the singular vectors with given weights are unique up to normalisation and consider the case when W0 is not diagonalisable among the singular vectors. ∗On leave from Institute for Theoretical Physics, Roland Eötvös University, H-1088 Budapest, Puskin u. 5-7, Hungary
منابع مشابه
Modules of the toroidal Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$
Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a new triangular decomposition. Singular vectors of Verma modules are determined using a similar condition with horizontal affine Lie subalgebras, and highest weight modules are described under the condition $c_1>0$ and $c_2=0$.
متن کاملSymbolic computation of the Duggal transform
Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...
متن کاملApproximating the Distributions of Singular Quadratic Expressions and their Ratios
Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...
متن کاملA Novel Noise Reduction Method Based on Subspace Division
This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...
متن کاملConstruction Formulae for Singular Vectors of the Topological N = 2 Superconformal Algebra
The Topological N=2 Superconformal algebra has 29 different types of singular vectors (in complete Verma modules) distinguished by the relative U(1) charge and the BRST-invariance properties of the vector and of the primary on which it is built. Whereas one of these types only exists at level zero, the remaining 28 types exist for general levels and can be constructed already at level 1. In thi...
متن کامل