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Differential calculus on quantized irreducible flag manifolds
Abstract
We give a new description of the differential calculus on the quantized irreducible flag manifold given by Heckenberger-Kolb. We also define a quantum analogue of the Dolbeault complex associated to an equivariant vector bundle on the irreducible flag manifold, and show that its cohomology groups coincide with the cohomology groups given by Andersen-Polo-Wen defined using the induction functor.
Related
- The intersection of two real flag manifolds in a complex flag manifold, and the canonical form of a compact symmetric triad
- Rational homotopy theory of flag manifolds
- CR Orbits on the complex flag manifolds of G2
- On topologically transitive subsets of flag manifolds
- Exotic involutions on irreducible 4-manifolds from Real Seiberg--Witten theory
BibTeX
@misc{tanisaki2026differential,
title = {{Differential calculus on quantized irreducible flag manifolds}},
author = {Toshiyuki Tanisaki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.13687},
eprint = {2609.13687},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13687},
}
RIS
TY - UNPB
TI - Differential calculus on quantized irreducible flag manifolds
AU - Toshiyuki Tanisaki
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.13687
UR - https://arxiv.org/abs/2609.13687
AB - We give a new description of the differential calculus on the quantized irreducible flag manifold given by Heckenberger-Kolb. We also define a quantum analogue of the Dolbeault complex associated to an equivariant vector bundle on the irreducible flag manifold, and show that its cohomology groups coincide with the cohomology groups given by Andersen-Polo-Wen defined using the induction functor.
ER -