Positivity conjecture for exceptional Hall coefficients

From papers

Let C{\mathcal C} be the cluster category under consideration, let MM be any object of C{\mathcal C}, let KK be an exceptional object of C{\mathcal C}, and let r(M,K)r(M,K) denote the Hall coefficient appearing in the exceptional Hall algebra multiplication.

Positivity conjecture. For any object MM and any exceptional object KK of C{\mathcal C}, the integer r(M,K)r(M,K) 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

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

Philippe Caldero and Bernhard Keller, “From triangulated categories to cluster algebras”, arXiv:math/0506018 (2005).

Solutions 0

No solutions have been posted yet.