Minuscule Elements of Weyl Groups: The Right Generalization of Young Diagrams
John Stembridge
University of Michigan (visiting MIT)
October 8,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

Dale Peterson has defined and studied what he calls "lambdaminuscule"
elements of (symmetrizable KacMoody) 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
many members.
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 lambdaminuscule element. This generalizes the famous hooklength
formula of FrameRobinsonThrall 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(atsign)math.mit.edu
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