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

E.M. MOENS, J. VAN DER JEUGT
2004 Lie Theory and Its Applications in Physics V  
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
more » ... zation of the character corresponding to the Z-grading of V λ . For a special choice of λ, the new t-dimension formula gives rise to a Hankel determinant identity.
doi:10.1142/9789812702562_0003 fatcat:qtonntn4wzeahg6mdvnuf6g3k4