Abstract |
|
Motivated by afine Schubert calculus,
we construct a family of dual graded graphs
(Γs,Γw)
for an arbitrary Kac–Moody algebra g. The graded graphs have the Weyl group
W of geh as vertex set and
are labeled versions of the strong and weak orders of
W respectively. Using a construction
of Lusztig for quivers with an admissible automorphism, we
define folded insertion for a Kac–Moody algebra and
obtain Sagan–Worley shifted insertion from
Robinson–Schensted insertion as a special case. Drawing on
work of Proctor and Stembridge, we analyze the induced subgraphs
of (Γs,Γw)
which are distributive posets.
|
Keywords
dual graded graphs, Schensted insertion, affine insertion
|
Mathematical Subject Classification
Primary: 05E10
Secondary: 57T15, 17B67
|
Authors
|
