Geodesic
A determinantal formula for supersymmetric Schur polynomials
Journal of Algebraic Combinatorics, Tome 17 (2003) no. 3, pp. 283-307.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We derive a new formula for the supersymmetric Schur polynomial $s \_$ lambda( x/y). The origin of this formula goes back to representation theory of the Lie superalgebra $g$l( m/n). In particular, we show how a character formula due to Kac and Wakimoto can be applied to covariant representations, leading to a new expression for s _ lambda( x/y). This new expression gives rise to a determinantal formula for s _ lambda( x/y). In particular, the denominator identity for $g$l( m/n) corresponds to a determinantal identity combining Cauchy's double alternant with Vandermonde's determinant. We provide a second and independent proof of the new determinantal formula by showing that it satisfies the four characteristic properties of supersymmetric Schur polynomials. A third and more direct proof ties up our formula with that of Sergeev-Pragacz.
Keywords: supersymmetric Schur polynomials, Lie superalgebra $gl( m/n)$, characters, covariant tensor representations, determinantal identities 
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     author = {Moens, E.M. and Van der Jeugt, J.},
     title = {A determinantal formula for supersymmetric {Schur} polynomials},
     journal = {Journal of Algebraic Combinatorics},
     pages = {283--307},
     publisher = {mathdoc},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2003__17_3_a3/}
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Moens, E.M.; Van der Jeugt, J. A determinantal formula for supersymmetric Schur polynomials. Journal of Algebraic Combinatorics, Tome 17 (2003) no. 3, pp. 283-307. http://geodesic.mathdoc.fr/item/JAC_2003__17_3_a3/