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Intermediate Wakimoto modules for affine \(\mathfrak{sl}(n+1, \mathbb C)\). (English) Zbl 1073.81048

Summary: We construct certain boson-type realizations of affine \({\mathfrak sl} (n+1, \mathbb C)\) that depend on a parameter \(0\leq r\leq n\) such that when \(r=0\) we get a Fock space realization appearing in [the first author, Algebr. Represent. Theory 8, No. 2, 173–206 (2005; Zbl 1122.17015)] and when \(r=n\) they are the Wakimoto modules described in the work of Feigin and Frenkel [B. L. Feigin and E. V. Frenkel, Usp. Mat. Nauk 43, No. 5 (263), 227–228 (1988; Zbl 0657.17013)].

MSC:

81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras