The crystal commutor and Drinfeld's unitarized \(R\)-matrix

DOI10.1007/s10801-008-0137-0zbMath1230.17008arXiv0707.2248OpenAlexW2064412790MaRDI QIDQ1016569

Peter Tingley, Joel Kamnitzer

Publication date: 6 May 2009

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.2248

zbMATH Keywords

quantum groupcrystal basisR-matrixcoboundary category

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items

Equivariant quantizations of symmetric algebras, Quantum groups, quantum tori, and the Grothendieck-Springer resolution, Remarks on quantum symmetric algebras, Universal K-matrices for quantum Kac-Moody algebras, Khovanov homology is a skew Howe 2-representation of categorified quantum \(\mathfrak{sl}_m\), Finite presentations for stated skein algebras and lattice gauge field theory, Mixed quantum skew Howe duality and link invariants of type \(A\), Coboundary categories and local rules, Invariant tensors and the cyclic sieving phenomenon, A formula for the 𝑅-matrix using a system of weight preserving endomorphisms, Crystals, quiver varieties, and coboundary categories for Kac-Moody algebras, Quantum flag manifolds, quantum symmetric spaces and their associated universal \(K\)-matrices, Peter-Weyl bases, preferred deformations, and Schur-Weyl duality

Cites Work

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• Crystals and coboundary categories
• Braided symmetric and exterior algebras
• Canonical Bases Arising from Quantized Enveloping Algebras. II
• Introduction to quantum groups