Polynomial Representation of $E_7$ and Its Combinatorial and PDE Implications
| dc.creator | Xu, Xiaoping | |
| dc.date | 2008-12-08 | |
| dc.date.accessioned | 2026-07-07T12:10:12Z | |
| dc.date.available | 2026-07-07T12:10:12Z | |
| dc.description | In this paper, we use partial differential equations to find the decomposition of the polynomial algebra over the basic irreducible module of $E_7$ into a sum of irreducible submodules. Moreover, we obtain a combinatorial identity, saying that the dimensions of certain irreducible modules of $E_7$ are correlated by the binomial coefficients of fifty-five. Furthermore, we prove that two families of irreducible submodules with three integral parameters are solutions of the fundamental invariant differential operator corresponding to Cartan's unique quartic $E_7$ invariant. | |
| dc.description | 37pages | |
| dc.identifier | https://arxiv.org/abs/0812.1432 | |
| dc.identifier | http://arxiv.org/abs/0812.1432 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209867 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B10, 17B25 | |
| dc.title | Polynomial Representation of $E_7$ and Its Combinatorial and PDE Implications | |
| dc.type | text |