Crystal Basis Theory for a Quantum Symmetric Pair $(\mathbf{U},\mathbf{U}^{\jmath })$

DOI10.1093/imrn/rny227zbMath1465.17016arXiv1704.01277OpenAlexW2963137836MaRDI QIDQ5854222

Hideya Watanabe

Publication date: 16 March 2021

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.01277

zbMATH Keywords

tensor productcrystal basisbipartitionintegrable modulequantized universal enveloping algebracoideal subalgebracanonical basiscompletely reduciblequantum symmetric pairVerma module, irreducible

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (10)

Classical weight modules over \(\imath\)quantum groups ⋮ Based modules over the \(\imath\) quantum group of type AI ⋮ Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras ⋮ Crystal bases of modified \(\imath\,\)quantum groups of certain quasi-split types ⋮ Finite Young wall model for representations of \(\imath\,\)quantum group \(\mathbf{U}^{\jmath}\) ⋮ A new tableau model for representations of the special orthogonal group ⋮ Polynomial functors and two-parameter quantum symmetric pairs ⋮ Cartan subalgebras for quantum symmetric pair coideals ⋮ Geometric Howe dualities of finite type ⋮ Quasi-split symmetric pairs of 𝑈(𝔰𝔩_{𝔫}) and Steinberg varieties of classical type

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