Representations of finite groups on Riemann-Roch spaces
| dc.creator | Joyner, David | |
| dc.creator | Traves, Will | |
| dc.date | 2002-10-26 | |
| dc.date | 2004-04-18 | |
| dc.date.accessioned | 2026-07-07T08:18:11Z | |
| dc.date.available | 2026-07-07T08:18:11Z | |
| dc.description | We study the action of a finite group on the Riemann-Roch space of certain divisors on a curve. If $G$ is a finite subgroup of the automorphism group of a projective curve $X$ over an algebraically closed field and $D$ is a divisor on $X$ left stable by $G$ then we show the irreducible constituents of the natural representation of $G$ on the Riemann-Roch space $L(D)=L_X(D)$ are of dimension $\leq d$, where $d$ is the size of the smallest $G$-orbit acting on $X$. We give an example to show that this is, in general, sharp (i.e., that dimension $d$ irreducible constituents can occur). Connections with coding theory, in particular to permutation decoding of AG codes, are discussed in the last section. Many examples are included. | |
| dc.description | 24 pages, significant revision | |
| dc.identifier | https://arxiv.org/abs/math/0210408 | |
| dc.identifier | http://arxiv.org/abs/math/0210408 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134344 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Information Theory | |
| dc.subject | Group Theory | |
| dc.subject | 14H37; 20C20; 94B27; 11T71; 05E20 | |
| dc.title | Representations of finite groups on Riemann-Roch spaces | |
| dc.type | text |