Knop F (2000)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2000
Publisher: Springer Verlag (Germany)
Book Volume: 6
Pages Range: 443-470
Journal Issue: 4
DOI: 10.1007/PL00001395
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 listing the combinatorial structure of multiplicity free actions.
APA:
Knop, F. (2000). Construction of commuting difference operators for multiplicity free spaces. Selecta Mathematica-New Series, 6(4), 443-470. https://dx.doi.org/10.1007/PL00001395
MLA:
Knop, Friedrich. "Construction of commuting difference operators for multiplicity free spaces." Selecta Mathematica-New Series 6.4 (2000): 443-470.
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