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2018

A Serre presentation for the $\imath$quantum groups

Chen, Xinhong, Lu, Ming, Wang, Weiqiang

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Let $(\bf U, \bf U^\imath)$ be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where "quasi-split" means the corresponding Satake diagram contains no black node.

We give a presentation of the $\imath$quantum group $\bf U^\imath$ with explicit $\imath$Serre relations.
The verification of new $\imath$Serre relations is reduced to some new q-binomial identities.
Consequently, $\bf U^\imath$ is shown to admit a bar involution under suitable conditions on the parameters.

A Serre presentation for the $\imath$quantum groups · Around

Built on

P. Terwilliger, The subconstituent algebra of an association scheme. III,
1993
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G. Letzter, Symmetric pairs for quantized enveloping algebras
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X. Chen, M. Lu and W. Wang, Serre-Lusztig relations for ı \imath quantum groups
Original
2001
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G. Letzter, Coideal subalgebras and quantum symmetric pairs
2002
Earlier work this paper cites.
G. Letzter, Quantum symmetric pairs and their zonal spherical functions
2003
Earlier work this paper cites.

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