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ON CHARACTERS AND DIMENSION FORMULAS FOR REPRESENTATIONS OF THE LIE SUPERALGEBRA gl(M|N)

2004
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Lie Theory and Its Applications in Physics V
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We derive a new expression for the supersymmetric Schur polynomials s λ (x/y). The origin of this formula goes back to representation theory of the Lie superalgebra gl(m|n) and gives rise to a determinantal formula for s λ (x/y). In the second part, we use this determinantal formula to derive new expressions for the dimension and superdimension of covariant representations V λ of the Lie superalgebra gl(m|n). In particular, we derive the t-dimension formula, giving a specialization of the

doi:10.1142/9789812702562_0003
fatcat:qtonntn4wzeahg6mdvnuf6g3k4