Quantum continuous \(\mathfrak{gl}_{\infty}\): tensor products of Fock modules and \(\mathcal{W}_{n}\)-characters. (English) Zbl 1278.17013

Summary: We construct a family of irreducible representations of the quantum continuous \(\mathfrak{gl}_{\infty}\) whose characters coincide with the characters of representations in the minimal models of the \(\mathcal {W}_{n}\)-algebras of \(\mathfrak{gl}_{n}\) type. In particular, we obtain a simple combinatorial model for all representations of the \(\mathcal{W}_{n}\)-algebras appearing in the minimal models in terms of \(n\) interrelating partitions.
This article continues the authors’ previous one [Kyoto J. Math. 51, No. 2, 337–364 (2011; Zbl 1278.17012)].


17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
05E10 Combinatorial aspects of representation theory


Zbl 1278.17012
Full Text: DOI arXiv


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