Defining relations for quantum symmetric pair coideals of Kac-Moody type

De Clercq Hadewijch

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Defining relations for quantum symmetric pair coideals of Kac-Moody type

机译：Defining relations for quantum symmetric pair coideals of Kac-Moody type

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摘要

Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra 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(g). We provide a complete presentation by generators and relations for these quantum symmetric pair coideal subalgebras. These relations are of inhomogeneous q-Serre type and are valid without restrictions on the generalized Cartan matrix. We draw special attention to the split case, where the quantum symmetric pair coideal subalgebras are generalized q-Onsager algebras.

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《journal of combinatorial algebra》 |2021年第4期|297-367|共71页
作者
De Clercq Hadewijch;
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Univ Ghent;

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正文语种英语
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Quantum groups; Kac-Moody algebras; quantum symmetric pairs; coideal sub-algebras; q-Onsager algebra; Serre presentation; Dolan-Grady relations; ZONAL SPHERICAL-FUNCTIONS; DOLAN-GRADY RELATIONS; ONSAGER ALGEBRA; AUTOMORPHISMS;

Defining relations for quantum symmetric pair coideals of Kac-Moody type

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