KR-polynomial and canonical-basis conjecture

Let (i,p)(i,p) and (i,s)(i,s) be vertices of the indicated folded Dynkin diagram with p<sp<s. Let m(i)[p,s]m^{(i)}[p,s] be the corresponding dominant monomial, let m(i)[p,s]\underline{m^{(i)}[p,s]} be its bar-invariant quantum monomial, and let FqF_q and LqL_q denote the KR-polynomial and canonical-basis element, respectively. KR-polynomial and canonical-basis conjecture. One has

Lq(m(i)[p,s])=Fq(m(i)[p,s]).L_q(\underline{m}^{(i)}[p,s])=F_q(\underline{m}^{(i)}[p,s]).

The claim proposes equality for this family of KR-polynomials; the supplied passage gives no resolution status.

Sources & referencesView supporting material

Primary source

Il-Seung Jang, Kyu-Hwan Lee and Se-jin Oh, “Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras”, arXiv:2304.07246 (2023).

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