Abstract
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”.
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