Positivity conjecture for exceptional Hall coefficients
Positivity conjecture for exceptional Hall coefficients
Let be the cluster category under consideration, let be any object of , let be an exceptional object of , and let denote the Hall coefficient appearing in the exceptional Hall algebra multiplication.
Positivity conjecture. For any object and any exceptional object of , the integer is nonnegative.
This is presented as an analogue of Lusztig's positivity theorem for the dual canonical basis and would give positivity for the relevant exceptional Hall algebra coefficients. The source provides no resolution of the claim.
Progress summary
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Sources & referencesView supporting material
Primary source
Philippe Caldero and Bernhard Keller, “From triangulated categories to cluster algebras”, arXiv:math/0506018 (2005).
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