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A Serre presentation for the imathquantum groups

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arxiv 1810.12475 v4 pith:F6CQK2I3 submitted 2018-10-30 math.RT math.QA

A Serre presentation for the imathquantum groups

classification math.RT math.QA
keywords imathquantumserrepresentationquasi-splitrelationsadmitarbitrary
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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