Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik–Zamolodchikov equations and Letzter–Kolb coideals

Kenny De Commer, Makoto Yamashita, Sergey Neshveyev, Lars Tuset

Onderzoeksoutput: Articlepeer review

16 Downloads (Pure)

Samenvatting

We establish an equivalence between two approaches to quantization of irreducible symmetric spaces of compact type within the framework of quasi-coactions, one based on the Enriquez-Etingof cyclotomic Knizhnik-Zamolodchikov (KZ) equations and the other on the Letzter-Kolb coideals. This equivalence can be upgraded to that of ribbon braided quasi-coactions, and then the associated reflection operators (K-matrices) become a tangible invariant of the quantization. As an application we obtain a Kohno-Drinfeld type theorem on type braid group representations defined by the monodromy of KZ-equations and by the Balagović-Kolb universal K-matrices. The cases of Hermitian and non-Hermitian symmetric spaces are significantly different. In particular, in the latter case a quasi-coaction is essentially unique, while in the former we show that there is a one-parameter family of mutually nonequivalent quasi-coactions.

Originele taal-2English
Artikelnummere14
Pagina's (van-tot)1-79
Aantal pagina's79
TijdschriftForum of Mathematics: Pi
Volume11
Nummer van het tijdschrift14
DOI's
StatusPublished - 2 mei 2023

Bibliografische nota

Funding Information:
The work of K.DC. was supported by the FWO grants G025115N and G032919N. The work of S.N. and M.Y. was partially supported by the NFR funded project 300837 ‘Quantum Symmetry’. M.Y. also acknowledges support by Grant for Basic Science Research Projects from The Sumitomo Foundation and JSPS Kakenhi 18K13421 at an early stage of collaboration.

Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.

Copyright:
Copyright 2023 Elsevier B.V., All rights reserved.

Vingerafdruk

Duik in de onderzoeksthema's van 'Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik–Zamolodchikov equations and Letzter–Kolb coideals'. Samen vormen ze een unieke vingerafdruk.

Citeer dit