Geodesic
Free field realizations of certain modules for affine Lie algebra $\widehat{sl}(n,\mathbb C)$
Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 28-52

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For the affine Lie algebra $\widehat{sl}(n,\mathbb C)$ we study a realization in terms of infinite sums of partial differential operators of a family of representations introduced in [BBFK]. These representations generalize a construction of Imaginary Verma modules [F1]. The realization constructed in the paper extends the free field realization of Imaginary Verma modules constructed by B. Cox [C1]. 
@article{ADM_2011_12_1_a2,
     author = {Renato A. Martins},
     title = {Free field realizations of certain modules for affine {Lie} algebra $\widehat{sl}(n,\mathbb C)$},
     journal = {Algebra and discrete mathematics},
     pages = {28--52},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a2/}
}
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Renato A. Martins. Free field realizations of certain modules for affine Lie algebra $\widehat{sl}(n,\mathbb C)$. Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 28-52. http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a2/