On non-integrable but “admissible” irreps of affine Lie algebras:
Victor G. Kac, Minoru Wakimoto, Modular invariant representations of infinite-dimensional Lie algebras and superalgebras, PNAS 85 14 (1988) 4956-4960 [doi:10.1073/pnas.85.14.4956]
Victor G. Kac, Minoru Wakimoto, Classification of modular invariant representations of affine algebras, p. 138-177 in V. G. Kač (ed.): Infinite dimensional Lie algebras and groups, Advanced series in Mathematical physics 7, World Scientific (1989) [pdf, cds:268092]
Victor G. Kac, Minoru Wakimoto, Modular and conformal invariance constraints in representation theory of affine algebras, Advances in Mathematics 70 2 (1988) 156-236 [doi:10.1016/0001-8708(88)90055-2, spire:275458]
Lecture notes on affine Lie algebras:
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