| Title:
|
Gradedness of the set of rook placements in $A_{n-1}$ (English) |
| Author:
|
Ignatev, Mikhail V. |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
171-182 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A rook placement is a subset of a root system consisting of positive roots with pairwise non-positive inner products. To each rook placement in a root system one can assign the coadjoint orbit of the Borel subgroup of a reductive algebraic group with this root system. Degenerations of such orbits induce a natural partial order on the set of rook placements. We study combinatorial structure of the set of rook placements in $A_{n-1}$ with respect to a slightly different order and prove that this poset is graded. (English) |
| Keyword:
|
Root system |
| Keyword:
|
rook placement |
| Keyword:
|
Borel subgroup |
| Keyword:
|
coadjoint orbit |
| Keyword:
|
graded poset |
| MSC:
|
06A07 |
| MSC:
|
17B08 |
| MSC:
|
17B22 |
| idZBL:
|
Zbl 07426416 |
| idMR:
|
MR4285749 |
| . |
| Date available:
|
2021-11-04T12:10:20Z |
| Last updated:
|
2021-12-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149187 |
| . |
| Reference:
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