Polynomial Representation of E6 and Its Combinatorial and PDE Implications
| dc.creator | Xu, Xiaoping | |
| dc.date | 2008-11-10 | |
| dc.date.accessioned | 2026-07-07T10:17:10Z | |
| dc.date.available | 2026-07-07T10:17:10Z | |
| dc.description | In this paper, we use partial differential equations to find the decomposition of the polynomial algebra over the basic irreducible module of E6 into a sum of irreducible submodules. It turns out that the cubic polynomial invariant corresponding to the Dicksons' invariant trilinear form is the unique fundamental invariant. Moreover, we obtain a combinatorial identity saying that the dimensions of certain irreducible modules of E6 are correlated by the binomial coefficients of twenty-six. Furthermore, we find all the polynomial solutions for the invariant differential operator corresponding to the Dickson trilinear form in terms of the irreducible submodules. | |
| dc.description | 24pages | |
| dc.identifier | https://arxiv.org/abs/0811.1399 | |
| dc.identifier | http://arxiv.org/abs/0811.1399 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173763 | |
| dc.subject | Representation Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 17B10, 17B25, 35c10 | |
| dc.title | Polynomial Representation of E6 and Its Combinatorial and PDE Implications | |
| dc.type | text |