Geodesic
On the various realizations of the basic representation of $A_{n-1}^{(1)}$ and the combinatorics of partitions
Journal of Algebraic Combinatorics, Tome 14 (2001) no. 2, pp. 133-144.

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Summary: The infinite dimensional Lie algebra $scirc$l $_{n} = A _{ n-1} ^{(1)}$ can be realized in several ways as an algebra of differential operators. The aim of this note is to show that the intertwining operators between the realizations of $scirc$l $_{n}$ corresponding to all partitions of $n$ can be described very simply by using combinatorial constructions.
Keywords: Lie algebras, representation theory, combinatorics of partitions, symmetric functions 
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     title = {On the various realizations of the basic representation of $A_{n-1}^{(1)}$ and the combinatorics of partitions},
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Leidwanger, Séverine. On the various realizations of the basic representation of $A_{n-1}^{(1)}$ and the combinatorics of partitions. Journal of Algebraic Combinatorics, Tome 14 (2001) no. 2, pp. 133-144. http://geodesic.mathdoc.fr/item/JAC_2001__14_2_a2/