Quantum symmetric pairs at roots of 1

@article{Bao2019QuantumSP,
  title={Quantum symmetric pairs at roots of 1},
  author={Huanchen Bao and Thomas M. Sale},
  journal={Advances in Mathematics},
  year={2019}
}
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We construct a bar involution for quantum symmetric pair coideal subalgebras $B_{\mathbf{c},\mathbf{s}}$ corresponding to involutive automorphisms of the second kind of symmetrizable Kac-Moody…

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We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satisfy a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of…

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0.1. An important role in the theory of modular representations is played by certain finite dimensional Hopf algebras u over Fp (the field with p elements, p = prime). Originally, u was defined…

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Abstract Let θ be an involution of a semisimple Lie algebra g , let g θ denote the fixed Lie subalgebra, and assume the Cartan subalgebra of g has been chosen in a suitable way. We construct a…

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We develop a general theory of canonical bases for quantum symmetric pairs $$({\mathbf{U}}, {\mathbf{U}}^\imath )$$(U,Uı) with parameters of arbitrary finite type. We construct new canonical bases…

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Apart from being of interest in its own right, the representation theory for quantum groups at roots of unity enters into Lusztig’s programme (see e.g. [Lus94]) for determining the irreducible…

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For quantum symmetric pairs $(\textbf {U}, \textbf {U}^\imath )$ of Kac–Moody type, we construct $\imath$-canonical bases for the highest weight integrable $\textbf U$-modules and their tensor…