Representation Theory of the Virasoro Algebra

Abstract

International audienc

Tensor product weight modules over the Virasoro algebra

“…The Virasoro algebra Vir is an infinite-dimensional Lie algebra over the complex numbers C, with basis {d n , C | n ∈ Z} and defining relations which is the universal central extension of the so-called infinite-dimensional Witt algebra. The algebra Vir is one of the most important Lie algebras both in mathematics and in mathematical physics; see, for example, [10,12] and references therein. In particular, it has been widely used in quantum physics [8], conformal field theory [3], Kac-Moody algebras [11,21], vertex operator algebras [4,7] and so on.…”

The 3-state Potts model and Rogers-Ramanujan series

“…Because of (9), any irreducible τ-twisted W 3 (4/5)-module is heavily constrained with respect to the spectrum of L(0). More precisely, The next result follows from the fusion rules for L(4/5 0) [16,22] (see also [14]). …”

Irreducible Twisted Heisenberg–Virasoro Modules from Tensor Products

“…[L m , L n ] = (n − m)L m+n + δ m+n,0 m 3 − m 12 C and [L m , C] = 0 for m, n ∈ Z, which is a one-dimensional central extension of the Witt algebra. It is well-known that L is a very important infinite-dimensional Lie algebra both in mathematics and mathematical physics (see, e.g., [7,8,10]). The theory of weight modules over L has been well developed (see [7]).…”

“…It is well-known that L is a very important infinite-dimensional Lie algebra both in mathematics and mathematical physics (see, e.g., [7,8,10]). The theory of weight modules over L has been well developed (see [7]). One of the most important weight modules is the highest weight module, which depends on the triangular decomposition structure of L. In fact, any irreducible weight module over the Virasoro algebra with a nonzero finite-dimensional weight space is a Harish-Chandra module (see [20]), whose weight subspaces are all finite-dimensional.…”