On the weak order of Coxeter groups

This paper provides some evidence for conjectural relations between extensions of (right) weak order on Coxeter groups, closure operators on root systems, and Bruhat order. The conjecture focused upon here refines an earlier question as to whether the set of initial sections of reflection orders, ordered by inclusion, forms a complete lattice. Meet and join in weak order are described in terms of a suitable closure operator. Galois connections are defined from the power set of W to itself, under which maximal subgroups of certain groupoids correspond to certain complete meet subsemilattices of weak order. An analogue of weak order for standard parabolic subsets of any rank of the root system is defined, reducing to the usual weak order in rank zero, and having some analogous properties in rank one (and conjecturally in general).Comment: 37 pages, submitte

Quelques nouvelles traditions de Pustozersk sur Avvakum

Malyšev Vladimir I. Quelques nouvelles traditions de Pustozersk sur Avvakum. In: Revue des études slaves, tome 45, fascicule 1-4, 1966. pp. 69-74

Avvakum suivant les traditions de Pustozersk

Malyšev Vladimir I., Alexandre Daniel. Avvakum suivant les traditions de Pustozersk. In: Revue des études slaves, tome 38, 1961. Mélanges Pierre Pascal. pp. 135-141

Notule V. Une communauté de vieux-croyants dans la Russie du Nord : l'Ermitage des Grandes-Prairies

Malyšev Vladimir, Pascal Pierre. Notule V. Une communauté de vieux-croyants dans la Russie du Nord : l'Ermitage des Grandes-Prairies. In: Revue des études slaves, tome 43, fascicule 1-4, 1964. pp. 83-89