On the double-affine Bruhat order: the $\epsilon =1$ conjecture and classification of covers in ADE type
Algebraic Combinatorics, Tome 2 (2019) no. 2, pp. 197-216.

For any Kac–Moody group $\mathbf{G}$, we prove that the Bruhat order on the semidirect product of the Weyl group and the Tits cone for $\mathbf{G}$ is strictly compatible with a $ℤ$-valued length function. We conjecture in general and prove for $\mathbf{G}$ of affine ADE type that the Bruhat order is graded by this length function. We also formulate and discuss conjectures relating the length function to intersections of “double-affine Schubert varieties”.

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DOI : https://doi.org/10.5802/alco.37
Classification : 05E10
Mots clés : Kac–Moody groups, double-affine Bruhat order
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Muthiah, Dinakar; Orr, Daniel. On the double-affine Bruhat order: the $\varepsilon =1$ conjecture and classification of covers in ADE type. Algebraic Combinatorics, Tome 2 (2019) no. 2, pp. 197-216. doi : 10.5802/alco.37. http://www.numdam.org/articles/10.5802/alco.37/

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