Journal of Lie Theory Vol. 14, No. 2, pp. 523535 (2004) 

On Dimension Formulas for $\g\l(m{}n)$ RepresentationsE. M. Moens and J. Van der JeugtE. M. Moens and J. Van der JeugtDepartment of Applied Mathematics and Computer Science Ghent University Krijgslaan 281S9 B9000 Gent Belgium ElsM.Moens@UGent.be Joris.VanderJeugt@UGent.be Abstract: We investigate new formulas for the dimension and superdimension of covariant representations $V_\lambda$ of the Lie superalgebra $\g\l(m{}n)$. The notion of $t$dimension is introduced, where the parameter $t$ keeps track of the $\Z$grading of $V_\lambda$. Thus when $t=1$, the $t$dimension reduces to the ordinary dimension, and when $t=1$ it reduces to the superdimension. An interesting formula for the $t$dimension is derived from a recently obtained new formula for the supersymmetric Schur polynomial $s_\lambda(x/y)$, which yields the character of $V_\lambda$. It expresses the $t$dimension as a simple determinant. For a special choice of $\lambda$, the new $t$dimension formula gives rise to a Hankel determinant identity. Full text of the article:
Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.
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