Closed or recursive descriptions of Z- and T-supports

Develop a closed or recursive formula that describes, for any coweight λ in Y^+, the Z-support of the basis element T_λ and the T-support of the element Z^λ in the Iwahori–Hecke algebra associated to a Kac–Moody root datum.

Background

Understanding how elements expressed in the Bernstein–Lusztig (Z) basis decompose in the Iwahori–Matsumoto (T) basis, and vice versa, is central to structural and computational aspects of Kac–Moody Hecke algebras.

While the paper proves triangularity and finiteness properties for these changes of basis, the authors note the absence of explicit closed or recursive formulas for the supports involved, indicating a gap in current knowledge.