A large family of indecomposable projective modules for the Khovanov-Kuperberg algebras of \(sl_3\)-webs (Q2872783)

A celebrated result of Khovanov is the categorification of the Jones polynomial of a tangle [\textit{M. Khovanov}, Algebr. Geom. Topol. 2, 665--741 (2002; Zbl 1002.57006)]. The paper under review is part of a programme to mimic Khovanov's construction for the Kuperberg bracket, that is a quantum invariant related to the representation theory of \(U_q(\mathfrak{sl}_3)\) [\textit{G. Kuperberg}, Commun. Math. Phys. 180, No. 1, 109--151 (1996; Zbl 0870.17005)]. To mimic Khovanov's \(U_q(\mathfrak{sl}_2)\) construction in the present \(U_q(\mathfrak{sl}_3)\) case requires the classification of indecomposable projective modules for certain algebras \(K^\epsilon\) [\textit{M. Mackaay}, \textit{W. Pan} and \textit{D. Tubbenhauer}, ``The \(\mathfrak{sl}_3\) web algebra'', \url{arXiv:1206.2118}]. The main result of this paper is to identify a certain family of indecomposable projective \(K^\epsilon\)-modules, with the goal of extending this family further in future work, and with the ultimate goal of classifying such modules.