Fullness conjecture for webs of type P in positive characteristic

Let \mathbbmk\mathbbm{k} be a field, and let \text{\boldmatha} \in \mathbbm{Z}^{r} and \text{\boldmathb} \in \mathbbm{Z}^{s} be the parameters indexing the relevant objects, with sizes |\text{\boldmatha}|andand|\text{\boldmathb}b\}|. Fullness conjecture. The fullness statement for the map in the web representation theory holds whenever

char(\mathbbmk)>\boldmatha+\boldmathb.\operatorname{char}(\mathbbm{k}) > |\text{\boldmath$a$}| + |\text{\boldmath$b$}|.

This conjecture gives a proposed characteristic bound under which the fullness result should remain valid; the supplied text does not state whether the conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Nicholas Davidson, Jonathan R. Kujawa and Robert Muth, “Webs of Type P”, arXiv:2109.03410 (2023).

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