1998/06/19 by Arne Meurman, Mirko Primc · 1 citation
Mathematics · #math.QA #msc:17B67 #msc:05A19
published as Memoirs Amer. Math. Soc., No. 652, 1999 · 83 pages, amstex
arxiv created 1998/06/19 · arxiv updated 2009/11/30
We show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra \goth g we construct the corresponding level k vertex operator algebra and we show that level k highest weight \goth g-modules are modules for this vertex operator algebra. We determine the set of annihilating fields of level k standard modules and we study the corresponding loop \goth g module---the set of relations that defines standard modules. In the case when \goth g is of type A1(1), we construct bases of standard modules parameterized by colored partitions and, as a consequence, we obtain a series of Rogers-Ramanujan type combinatorial identities.