Crystal bases of modified \(\imath\,\)quantum groups of certain quasi-split types

DOI10.1007/s10468-023-10207-zarXiv2110.07177OpenAlexW4380624470MaRDI QIDQ6151708

Hideya Watanabe

Publication date: 11 March 2024

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.07177

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Cites Work

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• Quantum symmetric Kac-Moody pairs
• \(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations
• Crystal bases of modified quantized enveloping algebra
• Canonical bases arising from quantum symmetric pairs
• Formulae of \(\iota\)-divided powers in \(\mathbf{U}_q(\mathfrak{sl}_2)\)
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• Symmetric pairs for quantized enveloping algebras
• Classical weight modules over \(\imath\)quantum groups
• Based modules over the \(\imath\) quantum group of type AI
• Crystal Bases
• Canonical Bases Arising from Quantized Enveloping Algebras
• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Canonical bases arising from quantum symmetric pairs of Kac–Moody type
• Crystal Basis Theory for a Quantum Symmetric Pair $(\mathbf{U},\mathbf{U}^{\jmath })$
• Introduction to quantum groups

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