Minuscule Elements of Weyl Groups: The Right Generalization of Young Diagrams
University of Michigan (visiting MIT)
refreshments at 3:45pm
Dale Peterson has defined and studied what he calls "lambda-minuscule"
elements of (symmetrizable Kac-Moody) Weyl groups. These elements can be
encoded by, or even identified with, a certain class of labeled partially
ordered sets. In type A, the posets are Young diagrams. In total, there
are 17 "irreducible" families of these posets, 16 of which have infinitely
As has become increasing clear in ongoing work of Robert Proctor,
there is an amazingly rich combinatorial theory hidden in these posets,
generalizing much of the classical combinatorics of Young diagrams.
For example, there is an explicit product formula, due to Peterson
(refined later by Proctor) for the number of reduced expressions for
any lambda-minuscule element. This generalizes the famous hooklength
formula of Frame-Robinson-Thrall for counting standard Young tableaux.
In this talk, we will survey the subject matter, including various
characterizations, classifications, and applications.
Speaker's Contact Info: jrs(at-sign)math.mit.edu
Return to seminar home page
Page loaded on September 27, 1999 at 02:17 PM.
Copyright © 1998-99, Sara C. Billey.
All rights reserved.