Geodesic
Classification of cocovers in the double affine Bruhat order
Amanda Welch1
1Eastern Illinois University
The electronic journal of combinatorics, Tome 29 (2022) no. 4

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Zbl DOI
We classify cocovers of a given element of the double affine Weyl semigroup $W_{\mathcal{T}}$ with respect to the Bruhat order, specifically when $W_{\mathcal{T}}$ is associated to a finite root system that is irreducible and simply laced. We do so by introducing a graphical representation of the length difference set defined by Muthiah and Orr and identifying the cocovering relations with the corners of those graphs. This new method allows us to prove that there are finitely many cocovers of each $x \in W_{\mathcal{T}}$. Further, we show that the Bruhat intervals in the double affine Bruhat order are finite.
DOI : 10.37236/10745
Classification : 05E16, 20F55, 06A07
Mots-clés : double affine Weyl semigroup, double affine Bruhat order

Amanda Welch  1

1 Eastern Illinois University 
Amanda Welch. Classification of cocovers in the double affine Bruhat order. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10745
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     author = {Amanda Welch},
     title = {Classification of cocovers in the double affine {Bruhat} order},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {4},
     doi = {10.37236/10745},
     zbl = {1503.05129},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10745/}
}
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