The Higher Transvectants are Redundant
| dc.creator | Abdesselam, Abdelmalek | |
| dc.creator | Chipalkatti, Jaydeep | |
| dc.date | 2008-01-10 | |
| dc.date.accessioned | 2026-07-07T08:53:37Z | |
| dc.date.available | 2026-07-07T08:53:37Z | |
| dc.description | Let A, B denote generic binary forms, and let u_r = (A,B)_r denote their r-th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the u_r. As a consequence, we show that each of the higher transvectants u_r, r>1, is redundant in the sense that it can be completely recovered from u_0 and u_1. This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of SL_2-representations, and the notion of a 9-j symbol from the quantum theory of angular momentum. We give explicit computational examples for SL_3, g_2 and S_5 to show that this result has possible analogues for other categories of representations. | |
| dc.description | LaTeX, 38 pages | |
| dc.identifier | https://arxiv.org/abs/0801.1533 | |
| dc.identifier | http://arxiv.org/abs/0801.1533 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145688 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 13A50; 22E70 | |
| dc.title | The Higher Transvectants are Redundant | |
| dc.type | text |