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The graded representations of affine Lie algebras. (English) Zbl 0761.17023
Geometry and physics, Proc. Winter Sch., Srni/Czech. 1990, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 26, 155-161 (1991).
[For the entire collection see Zbl 0742.00067.]
The author constructs new families of irreducible objects of a certain category $$K$$ which are not quotients of generalized Verma modules but have many analogous properties. The objects of $$K$$ constructed by parabolic induction were studied in [A. Rocha-Caridi, Lect. Notes Math. 933, 176-190 (1982; Zbl 0495.17009)]. First examples of such modules are built in this paper.
##### MSC:
 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations 17B70 Graded Lie (super)algebras 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)