The Harish-Chandra isomorphism for quantum \(\mathrm{GL}_2\)

DOI10.4171/JNCG/300zbMath1428.17012arXiv1603.09218OpenAlexW2313819901MaRDI QIDQ1711409

David Jordan, Martina Balagović

Publication date: 17 January 2019

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.09218

zbMATH Keywords

quantum groupsquantum differential operatorsdouble affine Hecke algebrafactorization homologyHarish-Chandra isomorphism

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Geometry of quantum groups (58B32)

Related Items

The 𝔤𝔩2-skein module of lens spaces via the torus and solid torus, A categorical approach to quantum moment maps, The finiteness conjecture for skein modules, Kauffman skein algebras and quantum Teichmüller spaces via factorization homology

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Hall algebra of an elliptic curve. I.
• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Torus knots and the rational DAHA
• Refined knot invariants and Hilbert schemes
• The HOMFLYPT skein algebra of the torus and the elliptic Hall algebra
• Local finiteness of the adjoint action for quantized enveloping algebras
• The diamond lemma for ring theory
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Quantum character varieties and braided module categories
• Quantizations of multiplicative hypertoric varieties at a root of unity
• Double affine Hecke algebras and Macdonald's conjectures
• The elliptic Hall algebra and the \(K\)-theory of the Hilbert scheme of \(\mathbb{A}^{2}\)
• The center of the reflection equation algebra via quantum minors
• A-polynomial, B-model, and quantization
• Fourier transform for quantum \(D\)-modules via the punctured torus mapping class group
• Quantized multiplicative quiver varieties.
• Quantum Riemann surfaces in Chern-Simons theory
• The A-polynomial from the noncommutative viewpoint
• Double affine Hecke algebras and generalized Jones polynomials
• Double affine Hecke algebras at roots of unity
• Jones Polynomials of Torus Knots via DAHA
• Skein modules and the noncommutative torus
• Invariant Differential Operators and an Homomorphism of Harish-Chandra