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

Fibered Schubert problems of Type I (from Section 3.1)

Schubert problems fibered over ⁴=2 on Gr(2,4) with Galois group S₂WrS₂ of order 8

Fiber: ˙˙˙˙ = 2  Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)        12422 18697 12256 6161        12490 18460 12409 6137        12348 18724 12333 6095         12246 18738 12322 6266         12434 18514 12285 6265         12447 18595 12486 6084         12395 18731 12248 6174         12500 18580 12334 6128         12504 18462 12312 6267          12459 18479 12522 6087          12308 18539 12501 6261          12239 18704 12431 6165          12506 18417 12480 6132          12526 18458 12327 6174          12397 18532 12545 6071          12654 18515 12276 6134           12554 18613 12227 6214           12495 18345 12368 6333           12500 18557 12353 6148           12307 18719 12303 6219            12639 18419 12399 6136

Fiber: ˙˙˙ = 2   Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)        12377 18560 12429 6143        12628 18505 12173 6245         12276 18475 12524 6237       12580 18408 12347 6132       12453 18635 12284 6144        12263 18639 12406 6238        12452 18385 12467 6203        12629 18638 12084 6232        12409 18651 12295 6167         12420 18504 12546 6141         12245 18523 12574 6167         12506 18528 12472 6084         12462 18614 12298 6117         12543 18526 12255 6228         12301 18636 12494 6075          12638 18458 12258 6263          12370 18629 12295 6255          12329 18531 12402 6318          12491 18392 12436 6228           12540 18368 12439 6176

Fiber: ˙˙˙  = 2  Schubert Problem (4) (2,2) (2,1,1) (1,1,1,1)       12516 18450 12409 6195       12448 18464 12419 6173       12294 18641 12216 6343        12397 18564 12434 6167        12330 18646 12316 6216        12403 18556 12254 6338        12634 18494 12315 6154        12486 18652 12126 6246        12427 18734 12355 6027        12204 18712 12396 6213        12317 18417 12604 6181         12473 18592 12283 6215         12427 18378 12605 6159         12271 18588 12475 6150         12445 18473 12556 6057         12278 18465 12530 6213         12371 18523 12410 6223         12476 18505 12467 6133         12493 18603 12328 6108         12514 18454 12496 6104         12440 18547 12285 6277          12516 18485 12404 6161          12474 18755 12301 6078          12482 18674 12142 6230          12518 18439 12446 6130           12392 18568 12381 6175

These are all fibered over 4=2 in Gr(2,4) with fiber ˙4=3 in Gr(2,5).
These have the same Galois group, S3WrS2, which has order 72
Schubert Problem	(6)	(4,2)	(3,3)	(3,2,1)	(3,1,1,1)	(2,2,2)	(2,2,1,1)	(2,1,1,1,1)	(1,1,1,1,1,1)
	8294	12324	2747	8240	2797	4165	6222	4061	665
	8286	12526	2659	8105	2627	4270	6251	4095	666
	8122	12511	2638	8291	2683	4211	6210	4167	686
	8341	12545	2740	8130	2673	4116	6120	4163	674
	8316	12325	2654	8159	2794	4182	6255	4125	681
	8453	12221	2727	8258	2704	4196	6206	4089	689
	8028	12345	2762	8194	2746	4227	6314	4276	673
	8301	12519	2708	8118	2768	4107	6168	4109	683
	8207	12497	2740	8167	2779	4112	6148	4199	711
	8309	12266	2735	8242	2766	4172	6273	4080	676
	8219	12346	2736	8189	2780	4184	6257	4154	685
	8306	12550	2638	8324	2704	4157	6096	4097	695
	8450	12251	2824	8306	2640	4190	6106	4156	665
	8409	12403	2682	8130	2785	4108	6182	4091	712
	8224	12412	2787	8231	2719	4166	6153	4237	633
	8367	12332	2783	8283	2749	4225	6066	4135	645
	8358	12458	2732	8171	2761	4140	6156	4066	724
	8309	12425	2782	8290	2809	4076	6222	4005	696
	8286	12437	2697	8316	2727	4186	6152	4077	685
	8321	12482	2678	8115	2751	4178	6084	4267	675
	8275	12451	2703	8194	2667	4105	6299	4172	691

These are all fibered over 4=2 in Gr(2,4) with fiber 6=5 in Gr(2,5).     These all have Galois group S5WrS2, which has order 28800
Schubert Problem	(10)	(8,2)	(6,4)	(6,2,2)	(5,5)	(5,4,1)	(5,3,2)	(5,3,1,1)	(5,2,2,1)	(5,2,1,1,1)	(5,1,1,1,1,1)	(4,4,2)	(4,4,1,1)	(4,3,2,1)	(4,3,1,1,1)	(4,2,2,2)	(4,2,2,1,1)	(4,2,1,1,1,1)	(4,1,1,1,1,1,1)	(3,3,2,2)	(3,3,2,1,1)	(3,3,1,1,1,1)	(3,2,2,2,1)	(3,2,2,1,1,1)	(3,2,1,1,1,1,1)	(3,1,1,1,1,1,1,1)	(2,2,2,2,2)	(2,2,2,2,1,1)	(2,2,2,1,1,1,1)	(2,2,1,1,1,1,1,1)	(2,1,1,1,1,1,1,1,1)	(1,1,1,1,1,1,1,1,1,1)
	5103	6058	4135	4139	908	2539	1599	1673	1207	831	78	3035	1528	2067	2072	2116	1536	1030	97	668	1384	677	1065	1747	709	60	214	391	541	233	27	7
	4976	6209	4226	4061	1018	2383	1636	1641	1321	798	85	3150	1542	2007	2040	2068	1521	1053	103	678	1388	680	1017	1735	752	74	206	371	550	192	28	1
	4887	6269	4163	4063	971	2488	1634	1673	1286	875	67	3123	1567	2051	2116	1980	1551	1020	115	654	1400	665	1026	1708	804	59	208	350	538	218	33	3
	5004	6135	4231	4184	951	2373	1620	1655	1252	809	91	3055	1552	2042	2081	2046	1570	1098	103	713	1345	663	1018	1739	757	61	221	362	502	223	40	1
	5073	6114	4102	4203	960	2428	1636	1698	1283	796	84	3028	1533	2027	2095	2049	1612	1037	113	707	1390	727	1004	1711	715	67	208	400	484	223	45	0
	5066	6080	4186	4149	987	2496	1577	1606	1232	818	80	3174	1571	2062	2071	2137	1535	992	98	636	1334	678	1062	1763	742	73	221	345	530	213	30	2
	4913	6278	4133	4242	1014	2466	1624	1598	1236	790	91	3088	1511	2061	2093	2053	1511	1036	110	707	1304	733	1019	1797	763	72	207	362	521	223	32	0
	4936	6333	4178	4114	993	2478	1647	1683	1241	816	71	3121	1556	2083	2022	1990	1467	1008	108	701	1374	693	1044	1684	771	55	201	391	512	220	46	1
	5086	6158	4126	4160	983	2440	1672	1684	1300	827	90	3057	1553	1980	2082	2044	1525	1078	81	649	1325	739	1017	1728	790	66	199	419	488	206	35	2

These all fibered over ˙3=2 in G(2,5) with fiber 4=2 in G(2,4), and have 4 solutions
These have the same Galois group, S2[S2], which has order 8
Schubert Problem	(4)	(2,2)	(2,1,1)	(1,1,1,1)
	12491	18442	12357	6267
	12503	18562	12329	6177
	12572	18495	12235	6238
	12496	18561	12390	6089
	12563	18476	12376	6151
	12356	18652	12401	6210
	12482	18385	12354	6303
	12385	18567	12368	6289

These all fibered over ˙4=3 in G(2,5) with fiber 4=2 in G(2,4), and have 6 solutions
These have the same Galois group, S2WrS3, which has order 48.
Schubert Problem	(6)	(4,2)	(4,1,1)	(3,3)	(2,2,2)	(2,2,1,1)	(2,1,1,1,1)	(1,1,1,1,1,1)
	8245	6251	6309	8215	7184	9215	3162	965
	8329	6246	6075	8370	7217	9116	3089	1048
	8192	6236	6188	8208	7167	9271	3163	1062
	8111	6140	6173	8539	7190	9328	3020	1066
	8268	6133	6295	8286	7149	9151	3149	1021
	8380	6158	6113	8340	7291	9164	3068	1028
	8256	6168	6204	8082	7264	9407	3071	1049
	8300	6323	6180	8212	7259	9258	3074	997
	8219	6241	6183	8331	7201	9327	3071	953
	8467	6076	6177	8296	7194	9273	3058	1041
	8240	6070	6176	8372	7275	9322	3057	1005
	8319	6225	6163	8084	7309	9345	3067	1050
	8240	6238	6265	8346	7181	9167	3089	995
	8256	6269	6266	8283	7116	9150	3129	1052
	8266	6124	6242	8202	7257	9303	3105	1033