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The quantum Frobenius for character varieties and multiplicative quiver varieties

Ganev, Iordan; Jordan, David; Safronov, Pavel (2020). The quantum Frobenius for character varieties and multiplicative quiver varieties. ArXiv.org 1901.11450, Cornell University.

Abstract

We prove that quantized multiplicative quiver varieties and quantum character varieties define sheaves of Azumaya algebras over the corresponding classical moduli spaces, and we prove that the Azumaya locus of the Kauffman bracket skein algebras contains the smooth locus, proving a strong form of the Unicity Conjecture of Bonahon and Wong. The proofs exploit a strong compatibility between quantum Hamiltonian reduction and the quantum Frobenius homomorphism as it arises in each setting. We therefore introduce the concepts of Frobenius quantum moment maps and their Hamiltonian reduction, and of Frobenius Poisson orders. We use these tools to construct canonical central subalgebras of quantum algebras, and explicitly compute the resulting Azumaya loci we encounter, using a natural nondegeneracy assumption.

Additional indexing

Item Type:Working Paper
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Language:English
Date:2020
Deposited On:12 Jan 2022 12:51
Last Modified:04 Jun 2024 12:42
Series Name:ArXiv.org
Number of Pages:64
ISSN:2331-8422
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.48550/arXiv.1901.11450
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