Bernstein-Gel’fand-Gel’fand resolution of \(W_3\) algebra in the lattice approach. (English) Zbl 0954.81503
Summary: We describe the embedding structure of the Verma modules of the \(W_3\) algebra using the free field representation (FFR) in the lattice approach. This structure is expressed by a set of intertwining diagrams. In particular, we show these diagrams can be used to carry out the Bernstein-Gelfand-Gelfand (BGG) resolution of the irreducible highest weight representation (IHWR) in terms of the Verma modules. As an application of prime importance, we show how the character of the \(W_3\) IHWR can be readily derived using the Rocha-Caridi procedure.
MSC:
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
