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On Dimension Formulas for gl ( m | n ) Representations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Moens, E. M. Jeugt, Joris Van Der |
| Copyright Year | 2004 |
| Abstract | We investigate new formulas for the dimension and superdimension of covariant representations Vλ of the Lie superalgebra gl(m|n). The notion of t -dimension is introduced, where the parameter t keeps track of the Z-grading of Vλ . 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 sλ(x/y), which yields the character of Vλ . It expresses the t -dimension as a simple determinant. For a special choice of λ , the new t -dimension formula gives rise to a Hankel determinant identity. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.maths.tcd.ie/EMIS/journals/JLT/vol.14_no.2/moensla2e.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
