|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Construction of commuting difference operators for multiplicity free spaces | | Friedrich Knop
; | | Date: |
1 Jun 2000 | | Journal: | Selecta Math. (N.S.) 6 (2000), 443-470 | | Subject: | Representation Theory; Combinatorics; Quantum Algebra MSC-class: 05E05 20G05 22E46 33C52 39A70 43A90 | math.RT math.CO math.QA | | Abstract: | We study root systems equipped with a basis of dominant weights such that certain axioms hold. This formalism allows to define a linear basis P of the space of Weyl group invariant polynomials. This basis is actually a family depending on at least one parameter. Our main result is the construction of difference operators which are simultaneously diagonalized by P. From this, Pieri type rules are derived. This generalizes results for shifted Jack polynomials. Even though the approach is purely combinatorial, the main motivation comes from multiplicity free actions of reductive groups on vector spaces. Then the algebra of invariant differential operators has a distinguished basis, the Capelli operators, which gives rise to a basis P as above. The paper ends with a comprehensive table detailing the combinatorial structure of multiplicity free actions. | | Source: | arXiv, math.RT/0006004 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER