Diagrams for symplectic type configurations

Citation
H. Cardenas et al., Diagrams for symplectic type configurations, COMM ALGEB, 27(7), 1999, pp. 3201-3210
Citations number
6
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
27
Issue
7
Year of publication
1999
Pages
3201 - 3210
Database
ISI
SICI code
0092-7872(1999)27:7<3201:DFSTC>2.0.ZU;2-U
Abstract
In [1] we gave a procedure that associates to each graph Gamma a configurat ion C(Gamma) of symplectic type. We called this graph "a diagram for the co nfiguration". In the same paper we prove that certain Dynkin-like diagrams (see Example 3 below) define the reduced symplectic configurations Sp(2m,2) ,O+(2m, 2) and O-(2m,2). In this note, using Hall's classification given in [2], we give diagrams fo r all symplectic type configurations (Theorem 1 and Remark), As an application we give a characterization of the universal representatio n for C(Gamma) and prove that our procedure defines the universal represent ation of C(Gamma).