ALGEBRAIC COMBINATORICS

no. 2

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

For any Kac–Moody group G, we prove that the Bruhat order on the semidirect product of the Weyl group and the Tits cone for G is strictly compatible with a ℤ-valued length function. We conjecture in general and prove for 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”.

Received:
Revised:
Accepted:
Published online:
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},
     pages = {197--216},
     publisher = {MathOA foundation},
     volume = {2},
     number = {2},
     year = {2019},
     doi = {10.5802/alco.37},
     mrnumber = {3934828},
     zbl = {1414.05304},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.37/}
}
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/articles/10.5802/alco.37/

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