no. 2
On the double-affine Bruhat order: the ε=1 conjecture and classification of covers in ADE type
Muthiah, Dinakar1 ; Orr, Daniel2
1 Department of Mathematics and Statistics Lederle Graduate Research Tower 1623D University of Massachusetts Amherst 710 N. Pleasant Street Amherst MA 01003-9305 (USA)
2 Department of Mathematics MC 0123 460 McBryde Hall Virginia Tech 225 Stanger St. Blacksburg VA 24061 (USA)
Algebraic Combinatorics, Tome 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”.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/alco.37
Classification : 05E10
Mots clés : Kac–Moody groups, double-affine Bruhat order
Muthiah, Dinakar 1 ; Orr, Daniel 2

1 Department of Mathematics and Statistics Lederle Graduate Research Tower 1623D University of Massachusetts Amherst 710 N. Pleasant Street Amherst MA 01003-9305 (USA)
2 Department of Mathematics MC 0123 460 McBryde Hall Virginia Tech 225 Stanger St. Blacksburg VA 24061 (USA) 
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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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