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Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators
KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.ORCID iD: 0000-0001-7481-2245
2019 (English)In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 51, no 2, p. 353-370Article in journal (Refereed) Published
Abstract [en]

We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials SP lambda((z1, horizontal ellipsis ,zn),(w1, horizontal ellipsis ,wm);theta) with respect to a natural positive semi-definite, but degenerate, Hermitian product ⟨center dot,center dot⟩n,m,theta '. In case m=0 (or n=0), our product reduces to Macdonald's well-known inner product ⟨center dot,center dot⟩n,theta ', and we recover his corresponding orthogonality results for the Jack polynomials P lambda((z1, horizontal ellipsis ,zn);theta). From our main results, we readily infer that the kernel of ⟨center dot,center dot⟩n,m,theta ' is spanned by the super-Jack polynomials indexed by a partition lambda not containing the mxn rectangle (mn). As an application, we provide a Hilbert space interpretation of the deformed trigonometric Calogero-Moser-Sutherland operators of type A(n-1,m-1).

Place, publisher, year, edition, pages
2019. Vol. 51, no 2, p. 353-370
National Category
Natural Sciences
Research subject
Mathematics; Physics
Identifiers
URN: urn:nbn:se:kth:diva-249098DOI: 10.1112/blms.12234ISI: 000462907600013OAI: oai:DiVA.org:kth-249098DiVA, id: diva2:1303798
Funder
Swedish Research Council, 2016-05167Stiftelsen Olle Engkvist Byggmästare, 184-0573
Note

QC 20190424

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-04-24Bibliographically approved

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Publisher's full texthttps://doi.org/10.1112/blms.12234

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Langmann, Edwin

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