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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, 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: 10.5802/alco.37
Classification: 05E10
Keywords: 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)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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, 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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