Opened 12 years ago
Closed 12 years ago
#6839 closed enhancement (fixed)
[with patch, positive review] Implementation of crystal of letters for type E7
Reported by: | aschilling | Owned by: | aschilling |
---|---|---|---|
Priority: | major | Milestone: | sage-4.1.2 |
Component: | combinatorics | Keywords: | combinat, crystals |
Cc: | sage-combinat | Merged in: | Sage 4.1.2.alpha1 |
Authors: | Anne Schilling, Brant Jones | Reviewers: | Daniel Bump |
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
- Implemented crystal of letters for type E7
- Added the method that goes to the highest weight element from any crystal element (living in a highest weight crystal)
Attachments (1)
Change History (7)
Changed 12 years ago by
comment:1 Changed 12 years ago by
- Cc sage-combinat added; sage-combinat-commits-bis@… removed
- Description modified (diff)
- Milestone changed from sage-4.1.2 to sage-combinat
- Owner changed from mhansen to aschilling
comment:2 Changed 12 years ago by
comment:3 Changed 12 years ago by
- Summary changed from Implementation of crystal of letters for type E7 to Implementation of crystal of letters for type E7 [with patch, positive review]
comment:4 Changed 12 years ago by
comment:5 Changed 12 years ago by
- Reviewers set to bump
comment:6 Changed 12 years ago by
- Merged in set to Sage 4.1.2.alpha1
- Milestone changed from sage-combinat to sage-4.1.2
- Resolution set to fixed
- Reviewers changed from bump to Daniel Bump
- Status changed from new to closed
- Summary changed from Implementation of crystal of letters for type E7 [with patch, positive review] to [with patch, positive review] Implementation of crystal of letters for type E7
The following docstring causes warnings when building the reference manual:
1287 TESTS:: 1288 1289 sage: C = CrystalOfLetters(['E',7]) 1290 sage: C.module_generators 1291 [[7]] 1292 sage: C.list() 1293 [[7], [-7, 6], [-6, 5], [-5, 4], [-4, 2, 3], [-2, 3], [-3, 1, 2], [-1, 1294 2], [-3, -2, 1, 4], [-1, -2, 4], [-4, 1, 5], [-4, -1, 3, 5], [-3, 5], 1295 [-5, 6, 1], [-5, -1, 3, 6], [-5, -3, 4, 6], [-4, 2, 6], [-2, 6], [-6, 7, 1296 1], [-1, -6, 3, 7], [-6, -3, 7, 4], [-6, -4, 2, 7, 5], [-6, -2, 7, 5], 1297 [-5, 7, 2], [-5, -2, 4, 7], [-4, 7, 3], [-3, 1, 7], [-1, 7], [-7, 1], 1298 [-1, -7, 3], [-7, -3, 4], [-4, -7, 2, 5], [-7, -2, 5], [-5, -7, 6, 2], 1299 [-5, -2, -7, 4, 6], [-7, -4, 6, 3], [-3, -7, 1, 6], [-7, -1, 6], [-6, 1300 2], [-2, -6, 4], [-6, -4, 5, 3], [-3, -6, 1, 5], [-6, -1, 5], [-5, 3], 1301 [-3, -5, 4, 1], [-5, -1, 4], [-4, 1, 2], [-1, -4, 3, 2], [-3, 2], [-2, 1302 -3, 4], [-4, 5], [-5, 6], [-6, 7], [-7], [-2, 1], [-2, -1, 3]] 1303 sage: C.check() 1304 True 1305 sage: all(b.f(i).e(i) == b for i in C.index_set() for b in C if b.f(i) is not None) 1306 True 1307 sage: all(b.e(i).f(i) == b for i in C.index_set() for b in C if b.e(i) is not None) 1308 True 1309 sage: G = C.digraph() 1310 sage: G.show(edge_labels=true, figsize=12, vertex_size=1)
See #6901 for a follow-up to this ticket.
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This patch creates the E7 crystal with highest weight vector the last fundamental weight. This is the 56-dimensional one. As usual, once the crystal of letters is implemented, others follow using CrystalOfTableaux?, though for such a large group this will be computationally intensive.
The patch applies without change to sage 4.1.1.
It passes
sage --testall
.I convinced myself that the crystal created is correct. For example, it branches correctly to E6, A6 and D6.
The new method to_highest_weight() is very useful. You can specify a subset of the index set and partition the crystal into subcrystals for any Levi subgroup.