PBW bases and marginally large tableaux in type D

Lusztig data of Kashiwara–Nakashima tableaux in types B and C

“…For other types, recall that there is another realization of Bp8q of type ABCD and type G 2 in terms of marginally large tableaux [8]. Recently, a simple combinatorial description of the isomorphism from the crystal of marginally large tableaux of type BCD to that of i-Lusztig data is obtained in [34,35] for some i which is different from our choice. Using the insertion scheme of BCD types, one may describe an embedding of KN λ into the crystal of marginally large tableaux to have an embedding from KN λ into B i , but it seems more involved than in type A (see Remark 5.10).…”