Séminaire Lotharingien de Combinatoire, 84B.75 (2020), 12 pp.
Kento Nakada
Order Structure of Shapes of Predominant Integral Weights and Cylindric Young Diagrams
Abstract.
In this paper, we give a generalization of d-complete posets to "infinite" d-complete posets.
Our infinite d-complete posets are realized as a subset of coroots on the Kac--Moody Lie algebra,
and has two different order relations in general.
One is the ordinary order on coroots.
The other is called heap order.
We give a sufficient condition for both orders to coincide.
As an application,
we give a multivariate hook formula for cylindric Young diagrams.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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