FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2593404493> ?p ?o ?g. }

• W2593404493 endingPage "90" @default.
• W2593404493 startingPage "80" @default.
• W2593404493 abstract "The classical Littlewood-Richardson rule (LR) describes the structure constants obtained when the cup product of two Schubert classes in the cohomology ring of a complex Grassmannian is written as a linear combination of Schubert classes. It also gives a rule for decomposing the tensor product of two irreducible polynomial representations of the general linear group into irreducibles, or equivalently, for expanding the product of two Schur S-functions in the basis of Schur S-functions. In this paper we give a short and self-contained argument which shows that this rule is a direct consequence of Pieri's formula (P) for the product of a Schubert class with a special Schubert class. There is an analogous Littlewood-Richardson rule for the Grassmannians which parametrize maximal isotropic subspaces of Cn, equipped with a symplectic or orthogonal form. The precise formulation of this rule is due to Stembridge (St), working in the context of Schur's Q-functions (S); the connection to geometry was shown by Hiller and Boe (HB) and Pragacz (Pr). The argument here for the type A rule works equally well in these more difficult cases and givesa simple derivation of Stembridge's rule from the Pieri formula of (HB). Currently there are many proofs available for the classical Littlewood-Richardson rule, some of them quite short. The proof of Remmel and Shimozono (RS) is also based on the Pieri rule; see the recent survey of van Leeuwen (vL) for alternatives. In contrast, we know of only two prior approaches to Stembridge's rule (described in (St, HH) and (Sh), respectively), both of which are rather involved. The argument presented here proceeds by defining an abelian group H with a basis of Schubert symbols, and a bilinear product on H with structure constants coming from the Littlewood-Richardson rule in each case. Since this rule is com- patible with the Pieri products, it suffices to show thatH is an associative algebra. The proof of associativity is based on Schutzenberger slides in type A, and uses the more general slides for marked shifted tableaux due to Worley (W) and Sagan (Sa) in the other Lie types. In each case, we need only basic properties of these operations which are easily verified from the definitions. Our paper is self-contained, once the Pieri rules are granted. The work on this article was completed during a fruitful visit to the Mathematisches Forschungsinstitut Oberwolfach, as part of the Research in Pairs program. It is a pleasure to thank the Institut for its hospitality and stimulating atmosphere." @default.
• W2593404493 created "2017-03-16" @default.
• W2593404493 creator A5054396668 @default.
• W2593404493 creator A5071870056 @default.
• W2593404493 creator A5072334254 @default.
• W2593404493 date "2004-06-01" @default.
• W2593404493 modified "2023-09-26" @default.
• W2593404493 title "Littlewood–Richardson rules for Grassmannians" @default.
• W2593404493 cites W1502147646 @default.
• W2593404493 cites W1993083418 @default.
• W2593404493 cites W1997886486 @default.
• W2593404493 cites W1999096883 @default.
• W2593404493 cites W2036568559 @default.
• W2593404493 cites W2046091890 @default.
• W2593404493 cites W2087792692 @default.
• W2593404493 cites W2156535181 @default.
• W2593404493 doi "https://doi.org/10.1016/s0001-8708(03)00165-8" @default.
• W2593404493 hasPublicationYear "2004" @default.
• W2593404493 type Work @default.
• W2593404493 sameAs 2593404493 @default.
• W2593404493 citedByCount "16" @default.
• W2593404493 countsByYear W25934044932012 @default.
• W2593404493 countsByYear W25934044932014 @default.
• W2593404493 countsByYear W25934044932015 @default.
• W2593404493 countsByYear W25934044932016 @default.
• W2593404493 countsByYear W25934044932017 @default.
• W2593404493 countsByYear W25934044932022 @default.
• W2593404493 crossrefType "journal-article" @default.
• W2593404493 hasAuthorship W2593404493A5054396668 @default.
• W2593404493 hasAuthorship W2593404493A5071870056 @default.
• W2593404493 hasAuthorship W2593404493A5072334254 @default.
• W2593404493 hasBestOaLocation W25934044932 @default.
• W2593404493 hasConcept C136119220 @default.
• W2593404493 hasConcept C202444582 @default.
• W2593404493 hasConcept C33923547 @default.
• W2593404493 hasConceptScore W2593404493C136119220 @default.
• W2593404493 hasConceptScore W2593404493C202444582 @default.
• W2593404493 hasConceptScore W2593404493C33923547 @default.
• W2593404493 hasIssue "1" @default.
• W2593404493 hasLocation W25934044931 @default.
• W2593404493 hasLocation W25934044932 @default.
• W2593404493 hasOpenAccess W2593404493 @default.
• W2593404493 hasPrimaryLocation W25934044931 @default.
• W2593404493 hasRelatedWork W1557945163 @default.
• W2593404493 hasRelatedWork W1985218657 @default.
• W2593404493 hasRelatedWork W2023661790 @default.
• W2593404493 hasRelatedWork W2073994398 @default.
• W2593404493 hasRelatedWork W2096753949 @default.
• W2593404493 hasRelatedWork W2963341196 @default.
• W2593404493 hasRelatedWork W3106133691 @default.
• W2593404493 hasRelatedWork W3124205579 @default.
• W2593404493 hasRelatedWork W3134646037 @default.
• W2593404493 hasRelatedWork W4249580765 @default.
• W2593404493 hasVolume "185" @default.
• W2593404493 isParatext "false" @default.
• W2593404493 isRetracted "false" @default.
• W2593404493 magId "2593404493" @default.
• W2593404493 workType "article" @default.