# Defining relations for quantum symmetric pair coideals of Kac–Moody type

@article{Clercq2019DefiningRF, title={Defining relations for quantum symmetric pair coideals of Kac–Moody type}, author={Hadewijch De Clercq}, journal={Journal of Combinatorial Algebra}, year={2019} }

Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra $\mathfrak{g}$, together with its subalgebra of fixed points under an involutive automorphism of the second kind. Quantum group analogs of this construction, known as quantum symmetric pairs, replace the fixed point Lie subalgebras by one-sided coideal subalgebras of the quantized enveloping algebra $U_q(\mathfrak{g})$. We provide a complete presentation by generators and relations for these quantum symmetric pair coideal…

## 4 Citations

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We introduce bivariate versions of the continuous q-Hermite polynomials. We obtain algebraic properties for them (generating function, explicit expressions in terms of the univariate ones, backward…

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This is a survey of some recent progress on quantum symmetric pairs and applications. The topics include quasi K-matrices, ıSchur duality, canonical bases, super Kazhdan-Lusztig theory, ıHall…

### Serre–Lusztig relations for $$\imath $$ ı quantum groups II

- MathematicsLetters in Mathematical Physics
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The $$\imath $$ ı Serre relations and the corresponding Serre–Lusztig relations are formulated and established for arbitrary $$\imath $$ ı quantum groups arising from quantum symmetric pairs of…

### Serre–Lusztig relations for ı quantum groups II

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The ı Serre relations and the corresponding Serre–Lusztig relations are formulated and established for arbitrary ı quantum groups arising from quantum symmetric pairs of Kac–Moody type.

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