A positive proof of the Littlewood-Richardson rule using the octahedron recurrence

Details A positive proof of the Littlewood-Richardson rule using the octahedron recurrence A positive proof of the Littlewood-Richardson rule using the octahedron recurrence

2003-06-18

arxiv.org/abs/math/0306274v1

Electron. J. Combin. 11 (2004), Research Paper 61

Mathematics

Combinatorics

15 pages, 12 figures

Scientific paper

We define the_hive ring_, which has a basis indexed by dominant weights for GL(n), and structure constants given by counting hives [KT1] (or equivalently honeycombs, or Berenstein-Zelevinsky patterns [BZ1]). We use the octahedron rule from [Robbins-Rumsey,Fomin-Zelevinsky,Propp,Speyer] to prove bijectively that this "ring" is indeed associative. This, and the Pieri rule, give a self-contained proof that the hive ring is isomorphic as a ring-with-basis to the representation ring of GL(n). In the honeycomb interpretation, the octahedron rule becomes "scattering" of the honeycombs. This recovers some of the "crosses and wrenches" diagrams from the very recent preprint [S], whose results we use to give a closed form for the associativity bijection.

Affiliated with

Also associated with

No associations

Rating

A positive proof of the Littlewood-Richardson rule using the octahedron recurrence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A positive proof of the Littlewood-Richardson rule using the octahedron recurrence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A positive proof of the Littlewood-Richardson rule using the octahedron recurrence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-51186