Analogue of the identity Log Det = Trace Log for resultants
| dc.creator | Morozov, A. | |
| dc.creator | Shakirov, Sh. | |
| dc.date | 2008-04-29 | |
| dc.date | 2008-05-20 | |
| dc.date.accessioned | 2026-07-07T09:39:33Z | |
| dc.date.available | 2026-07-07T09:39:33Z | |
| dc.description | Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for a system of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$ variables, just in the same way as determinant does for a system of linear equations. Because of this, resultants are important special functions of upcoming non-linear physics and begin to play a role in various topics related to string theory. Unfortunately, there is a lack of convenient formulas for resultants when the number of variables is large. To cure this problem, we generalize the well-known identity Log Det = Trace Log from determinants to resultants. The generalized identity allows to obtain explicit polynomial formulas for multidimensional resultants: for any number of variables, resultant is given by a Schur polynomial. We also give several integral representations for resultants, as well as a sum-over-paths representation. | |
| dc.description | 24 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0804.4632 | |
| dc.identifier | http://arxiv.org/abs/0804.4632 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161214 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Analogue of the identity Log Det = Trace Log for resultants | |
| dc.type | text |