For any Kac–Moody group , we prove that the Bruhat order on the semidirect product of the Weyl group and the Tits cone for is strictly compatible with a -valued length function. We conjecture in general and prove for 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:
Accepted:
Published online:
DOI: 10.5802/alco.37
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 = {http://www.numdam.org/articles/10.5802/alco.37/} }
TY - JOUR AU - Muthiah, Dinakar AU - Orr, Daniel TI - On the double-affine Bruhat order: the $\varepsilon =1$ conjecture and classification of covers in ADE type JO - Algebraic Combinatorics PY - 2019 SP - 197 EP - 216 VL - 2 IS - 2 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.37/ DO - 10.5802/alco.37 LA - en ID - ALCO_2019__2_2_197_0 ER -
%0 Journal Article %A Muthiah, Dinakar %A Orr, Daniel %T On the double-affine Bruhat order: the $\varepsilon =1$ conjecture and classification of covers in ADE type %J Algebraic Combinatorics %D 2019 %P 197-216 %V 2 %N 2 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.37/ %R 10.5802/alco.37 %G en %F 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. http://www.numdam.org/articles/10.5802/alco.37/
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