Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Coxeter transformation on Cominuscule Posets   Let $\mathsf{J(C)}$ be the poset of order ideals of a cominuscule poset
$\mathsf{C}$ where $\mathsf{C}$ comes from two of the three infinite families
of cominuscule posets or the exceptional cases. We show that the
Auslander-Reiten translation $\tau$ on the Grothendieck group of the bounded
derived category for the incidence algebra of the poset $\mathsf{J(C)}$, which
is called the \emph{Coxeter transformation} in this context, has finite order.
Specifically, we show that $\tau^{h+1}=\pm id$ where $h$ is the Coxeter number
for the relevant root system.

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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph