Journal
ADVANCES IN MATHEMATICS
Volume 267, Issue -, Pages 395-469Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2014.08.010
Keywords
Kac-Moody algebras; Involutions; Symmetric pairs; Quantum groups; Coideal subalgebras
Categories
Funding
- Maxwell Institute for Mathematical Sciences, Edinburgh
- Netherlands Organization for Scientific Research (NWO) within the VIDI-project Symmetry and modularity in exactly solvable models
- EPSRC [EP/K025384/1]
- Engineering and Physical Sciences Research Council [EP/K025384/1] Funding Source: researchfish
- EPSRC [EP/K025384/1] Funding Source: UKRI
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The present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac-Moody algebras. The resulting quantum symmetric pairs are right coideal subalgebras of quantized enveloping algebras. They give rise to triangular decompositions, including a quantum analog of the Iwasawa decomposition, and they can be written explicitly in terms of generators and relations. Moreover, their centers and their specializations are determined. The constructions follow G. Letzter's theory of quantum symmetric pairs for semisimple Lie algebras. The main additional ingredient is the classification of involutive automorphisms of the second kind of symmetrizable Kac-Moody algebras due to Kac and Wang. The resulting theory comprises various classes of examples which have previously appeared in the literature, such as q-Onsager algebras and the twisted q-Yangians introduced by Molev, Ragoucy, and Sorba. (C) 2014 Elsevier Inc. All rights reserved.
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