, Volume 16, Issue 1, pp 77–87 | Cite as

Upper Bounds in Affine Weyl Groups under the Weak Order

  • Debra J. Waugh


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 W0. In particular, we show that the quotient of W by W0 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.

affine Weyl groups parabolic quotients upper bounds weak ordering 


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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Debra J. Waugh
    • 1
  1. 1.Department of Science and MathematicsUniversity of Texas of the Permian BasinOdessaU.S.A.

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