"Row" (default): the original PieriMaps row-form basis. Source/target Schur modules are indexed by SSYTs as lists of weakly-increasing rows.
"Filling": the SchurFunctors column-form basis. Source/target are indexed by Fillings, with column-Garnir straightening relations. The matrix is obtained by post-hoc basis change with the equivariant iso pmToFilling.
"Weyl": the divided-power row-form basis. Source/target are indexed by WeylFillings. Numerically the same data as the Row matrix; it is just that the bases are interpreted on the Weyl (divided-power) side rather than the Schur side.
Use verifyWellDefined to verify that the chosen-convention map respects the appropriate straightening relations.
i1 : P = QQ[a,b,c];
i2 : pieri({2,1}, {1}, P, Convention => "Row")
o2 = | 2a 0 b 0 c 0 0 0 |
| 0 2a 0 b 0 c 0 0 |
| 0 0 0 a -a 0 2b c |
3 8
o2 : Matrix P <-- P