Matches in SemOpenAlex for { <https://semopenalex.org/work/W2092187650> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W2092187650 endingPage "102" @default.
- W2092187650 startingPage "33" @default.
- W2092187650 abstract "K. Aomoto has recently given a simple proof of an extension of A. Selberg's integral. We prove the following generalization of Aomoto's theorem. For eachk⩾0, there exists a family {skλ(t)} of homogeneous symmetric functions such that if the integrand of Selberg's integral is multiplied byskλ(t1, …, tn), then the integral has a certain closed form. Sinceskλ(t) is a renormalized Jack symmetric function withα=1/k, we call {skλ(t)} the Selberg–Jack symmetric functions. R. P. Stanley and I. G. Macdonald have extended many of the basic properties of the I. J. Schur functions to the Jack symmetric functions. Stanley's extensions of the Pieri formula, in a form obtained by Macdonald's extension of the duality property, and the combinatorial representation arise naturally in our proof. We give proofs of these and other results of Stanley and Macdonald. We give two constant-term identities which are equivalent to the integration formula. These results extend W. G. Morris' theorem forAnand the Macdonald–Morris constant term identity forBCn. By exploring Selberg's proof of his integral, we give a recurrence relation, outline a method for calculating the Selberg–Jack symmetric functions, and show that a constant term orthogonality relation, recently proved by Macdonald, arises naturally. We give an expansion which allows us to evaluate the normalization of this orthogonality, thus giving an alternative proof of the integration formula." @default.
- W2092187650 created "2016-06-24" @default.
- W2092187650 creator A5077638286 @default.
- W2092187650 date "1997-09-01" @default.
- W2092187650 modified "2023-10-17" @default.
- W2092187650 title "The Selberg–Jack Symmetric Functions" @default.
- W2092187650 cites W1566043079 @default.
- W2092187650 cites W1593259999 @default.
- W2092187650 cites W1975190722 @default.
- W2092187650 cites W1984039769 @default.
- W2092187650 cites W1987062201 @default.
- W2092187650 cites W1994361587 @default.
- W2092187650 cites W2008132457 @default.
- W2092187650 cites W2009751674 @default.
- W2092187650 cites W2016885814 @default.
- W2092187650 cites W2019586023 @default.
- W2092187650 cites W2066090378 @default.
- W2092187650 cites W2072972552 @default.
- W2092187650 cites W2087236732 @default.
- W2092187650 cites W2124818311 @default.
- W2092187650 cites W2168316830 @default.
- W2092187650 cites W2314376244 @default.
- W2092187650 cites W2607200564 @default.
- W2092187650 cites W4231201628 @default.
- W2092187650 cites W610831910 @default.
- W2092187650 doi "https://doi.org/10.1006/aima.1997.1642" @default.
- W2092187650 hasPublicationYear "1997" @default.
- W2092187650 type Work @default.
- W2092187650 sameAs 2092187650 @default.
- W2092187650 citedByCount "129" @default.
- W2092187650 countsByYear W20921876502012 @default.
- W2092187650 countsByYear W20921876502013 @default.
- W2092187650 countsByYear W20921876502014 @default.
- W2092187650 countsByYear W20921876502015 @default.
- W2092187650 countsByYear W20921876502016 @default.
- W2092187650 countsByYear W20921876502017 @default.
- W2092187650 countsByYear W20921876502018 @default.
- W2092187650 countsByYear W20921876502019 @default.
- W2092187650 countsByYear W20921876502020 @default.
- W2092187650 countsByYear W20921876502021 @default.
- W2092187650 countsByYear W20921876502022 @default.
- W2092187650 countsByYear W20921876502023 @default.
- W2092187650 crossrefType "journal-article" @default.
- W2092187650 hasAuthorship W2092187650A5077638286 @default.
- W2092187650 hasBestOaLocation W20921876501 @default.
- W2092187650 hasConcept C108710211 @default.
- W2092187650 hasConcept C114614502 @default.
- W2092187650 hasConcept C118539577 @default.
- W2092187650 hasConcept C134306372 @default.
- W2092187650 hasConcept C143432099 @default.
- W2092187650 hasConcept C17137986 @default.
- W2092187650 hasConcept C177148314 @default.
- W2092187650 hasConcept C199479865 @default.
- W2092187650 hasConcept C202444582 @default.
- W2092187650 hasConcept C2524010 @default.
- W2092187650 hasConcept C33923547 @default.
- W2092187650 hasConcept C3746008 @default.
- W2092187650 hasConceptScore W2092187650C108710211 @default.
- W2092187650 hasConceptScore W2092187650C114614502 @default.
- W2092187650 hasConceptScore W2092187650C118539577 @default.
- W2092187650 hasConceptScore W2092187650C134306372 @default.
- W2092187650 hasConceptScore W2092187650C143432099 @default.
- W2092187650 hasConceptScore W2092187650C17137986 @default.
- W2092187650 hasConceptScore W2092187650C177148314 @default.
- W2092187650 hasConceptScore W2092187650C199479865 @default.
- W2092187650 hasConceptScore W2092187650C202444582 @default.
- W2092187650 hasConceptScore W2092187650C2524010 @default.
- W2092187650 hasConceptScore W2092187650C33923547 @default.
- W2092187650 hasConceptScore W2092187650C3746008 @default.
- W2092187650 hasIssue "1" @default.
- W2092187650 hasLocation W20921876501 @default.
- W2092187650 hasOpenAccess W2092187650 @default.
- W2092187650 hasPrimaryLocation W20921876501 @default.
- W2092187650 hasRelatedWork W1991386078 @default.
- W2092187650 hasRelatedWork W2092187650 @default.
- W2092187650 hasRelatedWork W2135552440 @default.
- W2092187650 hasRelatedWork W2943281080 @default.
- W2092187650 hasRelatedWork W2945367033 @default.
- W2092187650 hasRelatedWork W2963744284 @default.
- W2092187650 hasRelatedWork W3086893517 @default.
- W2092187650 hasRelatedWork W3105057500 @default.
- W2092187650 hasRelatedWork W3183298406 @default.
- W2092187650 hasRelatedWork W4311623772 @default.
- W2092187650 hasVolume "130" @default.
- W2092187650 isParatext "false" @default.
- W2092187650 isRetracted "false" @default.
- W2092187650 magId "2092187650" @default.
- W2092187650 workType "article" @default.