Geodesic
Classifications of \(\Gamma\)-colored \(d\)-complete posets and upper \(P\)-minuscule Borel representations
Michael Strayer1
1Hampden–Sydney College
The electronic journal of combinatorics, Tome 28 (2021) no. 1
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The $\Gamma$-colored $d$-complete posets correspond to certain Borel representations that are analogous to minuscule representations of semisimple Lie algebras. We classify $\Gamma$-colored $d$-complete posets which specifies the structure of the associated representations. We show that finite $\Gamma$-colored $d$-complete posets are precisely the dominant minuscule heaps of J.R. Stembridge. These heaps are reformulations and extensions of the colored $d$-complete posets of R.A. Proctor. We also show that connected infinite $\Gamma$-colored $d$-complete posets are precisely order filters of the connected full heaps of R.M. Green.
DOI : 10.37236/9807
Classification : 05E10, 17B10, 17B67, 06A11, 06A07
Mots-clés : locally finite partially ordered sets, Dynkin diagram

Michael Strayer  1

1 Hampden–Sydney College 
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     title = {Classifications of {\(\Gamma\)-colored} \(d\)-complete posets and upper {\(P\)-minuscule} {Borel} representations},
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Michael Strayer. Classifications of \(\Gamma\)-colored \(d\)-complete posets and upper \(P\)-minuscule Borel representations. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/9807

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