Abstract: We present complete realization of irreducible -modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal superalgebras. We also provide an alternative Z-algebra approach to this construction. All irreducible highest weight -modules at the critical level are realized on the vector space where is the polynomial ring . Explicit combinatorial bases for these modules are also given.
Authors: Dražen Adamović, Naihuan Jing and Kailash C. Misra
Journal: Trans. Amer. Math. Soc. 369 (2017), 5113-5136
MSC (2010): Primary 17B69; Secondary 17B67, 17B68, 81R10
Published electronically: March 1, 2017