On the Dolbeault-Dirac operator of quantized symmetric spaces

DOI10.1112/tlms/tlv002zbMath1331.58012arXiv1307.7106OpenAlexW1934025394MaRDI QIDQ5501097

Ulrich Krähmer, Matthew Tucker-Simmons

Publication date: 12 August 2015

Published in: Transactions of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.7106

zbMATH Keywords

quantizationcompact Hermitian symmetric spacesDolbeault-Dirac operator

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Harmonic analysis on homogeneous spaces (43A85) Grassmannians, Schubert varieties, flag manifolds (14M15) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Spin and Spin({}^c) geometry (53C27) Geometry of quantum groups (58B32) Quantum groups (quantized function algebras) and their representations (20G42) Noncommutative geometry (à la Connes) (58B34) Quadratic and Koszul algebras (16S37)

Related Items (10)

Dolbeault-Dirac operators, quantum Clifford algebras and the Parthasarathy formula ⋮ An analogue of Weyl’s law for quantized irreducible generalized flag manifolds ⋮ A Dolbeault-Dirac spectral triple for the \(B_2\)-irreducible quantum flag manifold ⋮ A Hodge–de Rham Dirac operator on the quantum SU(2) ⋮ A Dolbeault-Dirac spectral triple for quantum projective space ⋮ On PBW-deformations of braided exterior algebras ⋮ Quantum flag manifolds, quantum symmetric spaces and their associated universal \(K\)-matrices ⋮ The Parthasarathy formula and a spectral triple for the quantum Lagrangian Grassmannian of rank two ⋮ On the Dolbeault-Dirac operators on quantum projective spaces ⋮ Positive line modules over the irreducible quantum flag manifolds

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