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Classifications of $\Gamma$-Colored $d$-Complete Posets and Upper $P$-Minuscule Borel Representations
2021
Electronic Journal of Combinatorics
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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
doi:10.37236/9807
fatcat:lrbf4bscmjepznvgjjmeuiinci