FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2034830023> ?p ?o ?g. }

• W2034830023 endingPage "37" @default.
• W2034830023 startingPage "25" @default.
• W2034830023 abstract "The author studied recently certain canonical bases for irreducible representations of quantum linear groups [5, 8]. The basic ingredients in the present work are the Kazhdan-Lusztig bases and cells for Hecke and q -Schur algebras [14, 4]. It has been proved that these canonical bases agree with Lusztig's canonical bases in the case of type A (see [8, 4.6]). Compared to Lusztig's definition of canonical bases, our construction in this case is more elementary and explicit in nature. This can also be seen from the link [8] of the canonical bases with Dipper-James' semistandard bases. Their relation is just like the relation between the ‘ T ’ basis and the ‘ C ’ basis for a Hecke algebra. Such a relation or such a pair of bases has been referred to as an IC relation or IC related bases in [6, 7]. IC related bases for the coordinate algebra of a quantum matrix semi-group have been introduced in [5] (see also [7]), where the basis of “standard” monomials is the analogous T -basis while the IC basis B is the union of the dual Kazhdan-Lusztig bases for q -Schur algebras. This paper considers a similar problem corresponding to the coordinate algebra of a quantum linear group. We shall construct a basis B̃ for such a coordinate algebra via the IC basis B for the quantum matrix semi-group with the property that it gives rise to the canonical bases of irreducible corepresentations. If this is the analogue of the ‘ C ’ basis for a Hecke algebra, what is the analogous basis corresponding to the ‘ T ’ basis? We shall show that an analogous basis may be defined via Dipper-Donkin's basis given in [2, (4.3.4)]. In fact, the basis B̃ and Dipper-Donkin's basis are quasi-IC related, that is, the transition matrices between them are the so-called quasi-pomatrices in the sense of [6, 1.2]. Thus the theory in [6, 2.2] allows us to introduce a new basis T for the coordinate algebra of quantum linear groups such that B̃ and T are IC related. Taking the images of B̃ and T , we shall obtain two bases B̃ 0 and T 0 for the coordinate algebra of the quantum special linear group and prove that they are IC related too. A second observation of the paper is that our basis B̃ is nothing but the dual basis of B́ , the canonical basis of the modified quantized enveloping algebra U introduced in [16, 17]. This is quite natural owing to the coincidence of the canonical bases for irreducible representations. Thus, we actually obtain a new (and dual) description for B in the case of type A ." @default.
• W2034830023 created "2016-06-24" @default.
• W2034830023 creator A5058107432 @default.
• W2034830023 date "1996-12-01" @default.
• W2034830023 modified "2023-09-24" @default.
• W2034830023 title "Global IC bases for quantum linear groups" @default.
• W2034830023 cites W1559169532 @default.
• W2034830023 cites W1981748961 @default.
• W2034830023 cites W1986067975 @default.
• W2034830023 cites W1991839009 @default.
• W2034830023 cites W2009190506 @default.
• W2034830023 cites W2011810388 @default.
• W2034830023 cites W2053086840 @default.
• W2034830023 cites W2053603290 @default.
• W2034830023 cites W2061657035 @default.
• W2034830023 cites W2066514041 @default.
• W2034830023 cites W2079614306 @default.
• W2034830023 cites W2123877559 @default.
• W2034830023 cites W2327336762 @default.
• W2034830023 doi "https://doi.org/10.1016/s0022-4049(96)00045-x" @default.
• W2034830023 hasPublicationYear "1996" @default.
• W2034830023 type Work @default.
• W2034830023 sameAs 2034830023 @default.
• W2034830023 citedByCount "11" @default.
• W2034830023 countsByYear W20348300232012 @default.
• W2034830023 countsByYear W20348300232013 @default.
• W2034830023 countsByYear W20348300232014 @default.
• W2034830023 crossrefType "journal-article" @default.
• W2034830023 hasAuthorship W2034830023A5058107432 @default.
• W2034830023 hasConcept C10628310 @default.
• W2034830023 hasConcept C106487976 @default.
• W2034830023 hasConcept C11252640 @default.
• W2034830023 hasConcept C121332964 @default.
• W2034830023 hasConcept C12426560 @default.
• W2034830023 hasConcept C128622974 @default.
• W2034830023 hasConcept C136119220 @default.
• W2034830023 hasConcept C148647251 @default.
• W2034830023 hasConcept C159985019 @default.
• W2034830023 hasConcept C172331165 @default.
• W2034830023 hasConcept C192562407 @default.
• W2034830023 hasConcept C202444582 @default.
• W2034830023 hasConcept C21736991 @default.
• W2034830023 hasConcept C2524010 @default.
• W2034830023 hasConcept C2781280181 @default.
• W2034830023 hasConcept C2781311116 @default.
• W2034830023 hasConcept C33923547 @default.
• W2034830023 hasConcept C41054515 @default.
• W2034830023 hasConcept C43562168 @default.
• W2034830023 hasConcept C62520636 @default.
• W2034830023 hasConcept C78540521 @default.
• W2034830023 hasConcept C84114770 @default.
• W2034830023 hasConceptScore W2034830023C10628310 @default.
• W2034830023 hasConceptScore W2034830023C106487976 @default.
• W2034830023 hasConceptScore W2034830023C11252640 @default.
• W2034830023 hasConceptScore W2034830023C121332964 @default.
• W2034830023 hasConceptScore W2034830023C12426560 @default.
• W2034830023 hasConceptScore W2034830023C128622974 @default.
• W2034830023 hasConceptScore W2034830023C136119220 @default.
• W2034830023 hasConceptScore W2034830023C148647251 @default.
• W2034830023 hasConceptScore W2034830023C159985019 @default.
• W2034830023 hasConceptScore W2034830023C172331165 @default.
• W2034830023 hasConceptScore W2034830023C192562407 @default.
• W2034830023 hasConceptScore W2034830023C202444582 @default.
• W2034830023 hasConceptScore W2034830023C21736991 @default.
• W2034830023 hasConceptScore W2034830023C2524010 @default.
• W2034830023 hasConceptScore W2034830023C2781280181 @default.
• W2034830023 hasConceptScore W2034830023C2781311116 @default.
• W2034830023 hasConceptScore W2034830023C33923547 @default.
• W2034830023 hasConceptScore W2034830023C41054515 @default.
• W2034830023 hasConceptScore W2034830023C43562168 @default.
• W2034830023 hasConceptScore W2034830023C62520636 @default.
• W2034830023 hasConceptScore W2034830023C78540521 @default.
• W2034830023 hasConceptScore W2034830023C84114770 @default.
• W2034830023 hasIssue "1" @default.
• W2034830023 hasLocation W20348300231 @default.
• W2034830023 hasOpenAccess W2034830023 @default.
• W2034830023 hasPrimaryLocation W20348300231 @default.
• W2034830023 hasRelatedWork W1924628035 @default.
• W2034830023 hasRelatedWork W2002902173 @default.
• W2034830023 hasRelatedWork W2022627393 @default.
• W2034830023 hasRelatedWork W2034830023 @default.
• W2034830023 hasRelatedWork W2045452781 @default.
• W2034830023 hasRelatedWork W2514884263 @default.
• W2034830023 hasRelatedWork W2953865351 @default.
• W2034830023 hasRelatedWork W2964119320 @default.
• W2034830023 hasRelatedWork W2964345926 @default.
• W2034830023 hasRelatedWork W4301479195 @default.
• W2034830023 hasVolume "114" @default.
• W2034830023 isParatext "false" @default.
• W2034830023 isRetracted "false" @default.
• W2034830023 magId "2034830023" @default.
• W2034830023 workType "article" @default.