FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2130849541> ?p ?o ?g. }

• W2130849541 endingPage "144" @default.
• W2130849541 startingPage "143" @default.
• W2130849541 abstract "In classical Lie group theory irreducible representation spaces are often decomposed into subspaces belonging to irreducible representations of a subgroup (or a chain of subgroups). Matrix elements of the representation w.r.t. a basis obtained in this way can often be expressed in terms of special functions. In particular, spherical functions are the matrix elements being left and right invariant w.r.t. a subgroup forming a Gelfand pair with the big group. An elementary example is the group SU(2) with diagonal subgroup isomorphic to U(1). Then the matrix elements of the irreducible representations of SU(2) w.r.t. a U(1)-basis can be expressed in terms of Jacobi polynomials and the spherical functions are Legendre polynomials. Nothing essential changes when we take the basis w.r.t. a subgroup conjugate to U(1), for instance SO(2). For quantum groups the situation is different. Only few quantum subgroups are available, in general, and we cannot take conjugates of quantum subgroups. For instance, quantum SU(2) has a quantum subgroup U(1) (an ordinary group), but no other nontrivial quantum subgroups are known and no conjugates of U(1) can be taken. The matrix elements of the irreducible representations of quantum SU(2) have been computed (cf. [5], [4], [1]) as little q-Jacobi polynomials and the spherical matrix elements as little q-Legendre polynomials. (See Koelink & Koornwinder’s q-special functions tutorial in these Proceedings.) In order to say something about the missing conjugates of a quantum subgroup, we use the quantized universal enveloping algebra. Let U = Uq(sl(2)) be the algebra generated by A, A, B, C with relations AA = 1 = AA, AB = qBA, AC = qCA, [B,C] = (A − A)/(q − q). U becomes a Hopf algebra with comultiplication ∆(A) = A⊗A, ∆(B) = A⊗B+B⊗A, ∆(C) = A⊗ C + C ⊗A. Call X ∈ U twisted primitive if ∆(X) = A⊗X +X ⊗ A. Then X has this property iff X ia a linear combination of A − A, B and C. This three-dimensional space is a kind of quantum analogue of the Lie algebra sl(2). The Hopf ∗-algebra A of “polynomial functions” on quantum SU(2) is in doubly non-degenerate Hopf algebra duality with U . Call a ∈ A left (right) invariant w.r.t. a twisted primitive element X ∈ U if (X ⊗ id)(∆(a)) = 0 (respectively (id⊗X)(∆(a)) = 0)." @default.
• W2130849541 created "2016-06-24" @default.
• W2130849541 creator A5087068510 @default.
• W2130849541 date "1992-01-01" @default.
• W2130849541 modified "2023-09-30" @default.
• W2130849541 title "𝑞-special functions and their occurrence in quantum groups" @default.
• W2130849541 cites W2042945816 @default.
• W2130849541 cites W2046283839 @default.
• W2130849541 cites W2138018765 @default.
• W2130849541 doi "https://doi.org/10.1090/conm/134/1187286" @default.
• W2130849541 hasPublicationYear "1992" @default.
• W2130849541 type Work @default.
• W2130849541 sameAs 2130849541 @default.
• W2130849541 citedByCount "8" @default.
• W2130849541 countsByYear W21308495412013 @default.
• W2130849541 crossrefType "other" @default.
• W2130849541 hasAuthorship W2130849541A5087068510 @default.
• W2130849541 hasBestOaLocation W21308495412 @default.
• W2130849541 hasConcept C114614502 @default.
• W2130849541 hasConcept C121332964 @default.
• W2130849541 hasConcept C136119220 @default.
• W2130849541 hasConcept C142292226 @default.
• W2130849541 hasConcept C148647251 @default.
• W2130849541 hasConcept C202444582 @default.
• W2130849541 hasConcept C33923547 @default.
• W2130849541 hasConcept C62520636 @default.
• W2130849541 hasConcept C84114770 @default.
• W2130849541 hasConceptScore W2130849541C114614502 @default.
• W2130849541 hasConceptScore W2130849541C121332964 @default.
• W2130849541 hasConceptScore W2130849541C136119220 @default.
• W2130849541 hasConceptScore W2130849541C142292226 @default.
• W2130849541 hasConceptScore W2130849541C148647251 @default.
• W2130849541 hasConceptScore W2130849541C202444582 @default.
• W2130849541 hasConceptScore W2130849541C33923547 @default.
• W2130849541 hasConceptScore W2130849541C62520636 @default.
• W2130849541 hasConceptScore W2130849541C84114770 @default.
• W2130849541 hasLocation W21308495411 @default.
• W2130849541 hasLocation W21308495412 @default.
• W2130849541 hasOpenAccess W2130849541 @default.
• W2130849541 hasPrimaryLocation W21308495411 @default.
• W2130849541 hasRelatedWork W1200165358 @default.
• W2130849541 hasRelatedWork W1499886697 @default.
• W2130849541 hasRelatedWork W1959487056 @default.
• W2130849541 hasRelatedWork W1972012307 @default.
• W2130849541 hasRelatedWork W2023264675 @default.
• W2130849541 hasRelatedWork W2030982655 @default.
• W2130849541 hasRelatedWork W2077715243 @default.
• W2130849541 hasRelatedWork W2094818705 @default.
• W2130849541 hasRelatedWork W2249345580 @default.
• W2130849541 hasRelatedWork W2315248794 @default.
• W2130849541 hasRelatedWork W2483000307 @default.
• W2130849541 hasRelatedWork W2582608621 @default.
• W2130849541 hasRelatedWork W2798310373 @default.
• W2130849541 hasRelatedWork W2951958632 @default.
• W2130849541 hasRelatedWork W2963204460 @default.
• W2130849541 hasRelatedWork W3004031069 @default.
• W2130849541 hasRelatedWork W3092904806 @default.
• W2130849541 hasRelatedWork W3098557890 @default.
• W2130849541 hasRelatedWork W3104651272 @default.
• W2130849541 hasRelatedWork W73335431 @default.
• W2130849541 isParatext "false" @default.
• W2130849541 isRetracted "false" @default.
• W2130849541 magId "2130849541" @default.
• W2130849541 workType "other" @default.