Enriched Schubert Galois groups in the Grassmannian G(4,9)

Abraham Martín del Campo, Frank Sottile, and Robert Williams.

Non reduced enriched Schubert problems

Five Schubert problems were not reduced, coming from Schubert problems in G(4,8). One reduces to Derksen's problem.

This nonreduced problem has Galois group S4 and six solutions
Schubert Problem (4,2) (3,3) (2,2,1,1) (1,1,1,1,1,1)Reduction
      12486 16539 18426 2109      

The other four reduce to Schubert problems in G(4,8) that are fibrations of type II.

These have the same Galois group, S2[S2], which has order 8
Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)Reduction
      12455 18577 12465 6067     
       12438 18580 12374 6175      
       12559 18666 12149 6174      
        12579 18538 12307 6131       
Work of Sottile supported by the National Science Foundation under Grant DMS-1501370.
Last modified: Sun Feb 3 11:45:32 CST 2019