N>=2 symmetric superpolynomials
| Autor: | Alarie-Vézina, L., Lapointe, L., Mathieu, P. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Physics 58, 033503 (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.4976741 |
| Popis: | The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N=1 supersymmetric version of the classical bases of symmetric functions. Here we consider the case where two independent anticommuting variables are attached to each ordinary variable. The N=2 super-version of the monomial, elementary, homogeneous symmetric functions, as well as the power sums, are then constructed systematically (using an exterior-differential formalism for the multiplicative bases), these functions being now indexed by a novel type of superpartitions. Moreover, the scalar product of power sums turns out to have a natural N=2 generalization which preserves the duality between the monomial and homogeneous bases. All these results are then generalized to an arbitrary value of N. Finally, for N=2, the scalar product and the homogenous functions are shown to have a one-parameter deformation, a result that prepares the ground for the yet-to-be-defined N=2 Jack superpolynomials. Comment: 36 pages |
| Databáze: | arXiv |
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