# ALGEBRAIC COMBINATORICS

On the double-affine Bruhat order: the $\epsilon =1$ conjecture and classification of covers in ADE type
Algebraic Combinatorics, Volume 2 (2019) no. 2, p. 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”.
Revised : 2018-05-24
Accepted : 2018-07-23
Published online : 2019-03-05
DOI : https://doi.org/10.5802/alco.37
Classification:  05E10
Keywords: Kac–Moody groups, double-affine Bruhat order
@article{ALCO_2019__2_2_197_0,
author = {Muthiah, Dinakar and Orr, Daniel},
title = {On the double-affine Bruhat order: the $\varepsilon =1$ conjecture and classification of covers in ADE type},
journal = {Algebraic Combinatorics},
publisher = {MathOA foundation},
volume = {2},
number = {2},
year = {2019},
pages = {197-216},
doi = {10.5802/alco.37},
language = {en},
url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_2_197_0}
}

Muthiah, Dinakar; Orr, Daniel. On the double-affine Bruhat order: the $\varepsilon =1$ conjecture and classification of covers in ADE type. Algebraic Combinatorics, Volume 2 (2019) no. 2, pp. 197-216. doi : 10.5802/alco.37. https://alco.centre-mersenne.org/item/ALCO_2019__2_2_197_0/

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