Quantum Weyl group and a multiplicative formula for the R-matrix of a simple Lie algebra

DOI10.1007/BF01079599zbMath0729.17010OpenAlexW1972255008WikidataQ115394259 ScholiaQ115394259MaRDI QIDQ805724

Ya. S. Sojbel'man, Sergei Levendorskii

Publication date: 1991

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01079599

zbMATH Keywords

tensor product spaceunitary groupsymmetric groupirreducible representations

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Applications of linear algebraic groups to the sciences (20G45)

Related Items (19)

Categorical geometric skew Howe duality ⋮ Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity ⋮ Quantum dynamical coboundary equation for finite dimensional simple Lie algebras ⋮ Manin triples and differential operators on quantum groups ⋮ Existence of R-matrix for a quantized Kac–Moody algebra ⋮ A cluster realization of \(U_q(\mathfrak {sl}_{\mathfrak {n}})\) from quantum character varieties ⋮ Khoroshkin-Tolstoy approach to quantum superalgebras ⋮ Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra ⋮ \(\mathbb Z/2\mathbb Z\)-extensions of Hopf algebra module categories by their base categories ⋮ Combinatorial aspects of the quantized universal enveloping algebra of \(\mathfrak {sl}_{n+1}\) ⋮ Coherent states for quantum compact groups ⋮ Hopf algebras with trace and representations ⋮ The R-matrix of quantum doubles of Nichols algebras of diagonal type ⋮ Baxter \(Q\)-operator from quantum \(K\)-theory ⋮ A formula for the 𝑅-matrix using a system of weight preserving endomorphisms ⋮ R-matrix and inverse Shapovalov form ⋮ The crystal commutor and Drinfeld's unitarized \(R\)-matrix ⋮ Quantum flag manifolds, quantum symmetric spaces and their associated universal \(K\)-matrices ⋮ La R-matrice pour les algèbres quantiques de type affine non tordu1

Cites Work

• Unnamed Item
• An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
• Quantum deformations of certain simple modules over enveloping algebras
• Poisson manifolds and the Schouten bracket

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