HomogeneousTools is a toolset to work with homogeneous varieties and homogeneous vector bundles on them, mostly with a view towards sheaf cohomology.
Recent posts
- 2026/08/16 Semisimple.jl 1.3.0
- 2026/08/16 ZeroLocus62, a label format for zero loci
- 2026/08/13 PartialFlagVarieties.jl 0.3.1
- 2026/07/17 PartialFlagVarieties.jl, a first pre-release
- 2026/06/15 Representations with the same degree: smallest collisions
- 2026/06/04 Representations with the same degree
- 2026/05/29 Verifying Kostant’s conjecture using Semisimple.jl
- 2026/05/12 Lie.jl is now Semisimple.jl
- 2026/05/11 Lie.jl 1.0.0 is out
- 2026/05/08 HomogeneousTools is now live
Semisimple.jl
A Julia package for computations with semisimple Lie algebras: root systems, Weyl groups, weight lattices, and representation-theoretic operations.
It is similar to LiE and LieART, with a heavy focus on speed. It does not yet match the features of these packages, but the basics are there.
PartialFlagVarieties.jl
A Julia package for computing with partial flag varieties $G/P$: equivariant vector bundles, sheaf cohomology via the Borel–Weil–Bott theorem, zero loci, Hodge numbers, Hochschild cohomology, exceptional collections, and more.
PartialFlagVarieties.jl is now available as a public pre-release, v0.1.0. The essential functionality is in place and ready to use, but the API may still change before a stable 1.0 release. See the announcement post for what works today and what is still coming.
ZeroLocus62
ZeroLocus62 is a compact, canonical encoding for bundles, zero loci, and degeneracy loci of completely reducible vector bundles on partial flag varieties.
It allows one to say 40.G
and this encodes a quintic threefold in a succinct way.
A more complicated example would be 603.111,
the Fano 3-fold 1-10:
the zero locus of $(\bigwedge^2 \mathcal{U}^\vee)^{\oplus 3}$ on $\mathrm{Gr}(3,7)$.
Such a data format is very useful for efficiently encoding zero loci and communicating about them across systems.