NDLI: Upper Bounds in Affine Weyl Groups under the Weak Order

Content Provider	Springer Nature Link
Author	Waugh, Debra J.
Copyright Year	1999
Abstract	Björner and Wachs proved that under the weak order every quotient of a Coxeter group is a meet semi-lattice, and in the finite case is a lattice. In this paper, we examine the case of an affine Weyl group W with corresponding finite Weyl group W $_{0}$. In particular, we show that the quotient of W by W $_{0}$ is a lattice and that up to isomorphism this is the only quotient of W which is a lattice. We also determine that the question of which pairs of elements of W have upper bounds can be reduced to the analogous question within a particular finite subposet.
Starting Page	77
Ending Page	87
Page Count	11
File Format	PDF
ISSN	01678094
Journal	Order
Volume Number	16
Issue Number	1
e-ISSN	15729273
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1999-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theory of Computation Geometry Convex and Discrete Geometry
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Theory and Mathematics Geometry and Topology

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Upper Bounds in Affine Weyl Groups under the Weak Order