Quantum continuous $\mathfrak{gl}_{\infty}$ : Tensor products of Fock modules and $\mathcal{W}_{n}$ -characters
Feigin, B. ; Feigin, E. ; Jimbo, M. ; Miwa, T. ; Mukhin, E.
Kyoto J. Math., Tome 51 (2011) no. 1, p. 365-392 / Harvested from Project Euclid
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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.
Publié le : 2011-05-15
Classification:  17B37,  81R10,  05E10 
@article{1303494507,
     author = {Feigin, B. and Feigin, E. and Jimbo, M. and Miwa, T. and Mukhin, E.},
     title = {Quantum continuous $\mathfrak{gl}\_{\infty}$ : Tensor products of Fock modules and $\mathcal{W}\_{n}$ -characters},
     journal = {Kyoto J. Math.},
     volume = {51},
     number = {1},
     year = {2011},
     pages = { 365-392},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303494507}
}

Feigin, B.; Feigin, E.; Jimbo, M.; Miwa, T.; Mukhin, E. Quantum continuous $\mathfrak{gl}_{\infty}$ : Tensor products of Fock modules and $\mathcal{W}_{n}$ -characters. Kyoto J. Math., Tome 51 (2011) no. 1, pp.  365-392. http://gdmltest.u-ga.fr/item/1303494507/