Dear Kshipra, Thank you for your interest in doing GSoC with SageMath. Please be aware that Verma modules and simple modules (in BBG category O) for simple Lie algebras have already been implemented in SageMath. In principle, that implementation also works for affine Lie algebras (I think it might just need to be enabled; I haven't actually tried testing it yet). Manipulating branching rules and multiplicities for simple Lie algebras is done by the WeylCharacterRing. Quantum groups and their irreps for simple Lie algebras are available through GAP's QuaGroup package.
The problem is that these implementations are fairly slow and heavy-handed for the finite dimensional simples (even for small rank/dimensional cases). Some of this I know how to deal with (the PBW basis is slow due to how it currently handles ordering elements). Furthermore, the class structure of all of these representations is not really connected and has code duplication. Some of the things I would like to see, beyond fixing the aforementioned problems, would be - parabolic Verma modules and morphisms between them - Kirillov-Reshetikhin modules (or at least fundamental) and fusion products - simples for the Virasoro algebra There's a lot of math involved with all of these, and there are parts that are not well developed with an algorithmic approach. So that is something to be careful about. Anyways, it is your project and your proposal. So please write your proposal with what you would want to do and think would benefit SageMath (and its users). Best, Travis On Monday, March 31, 2025 at 2:47:09 PM UTC+9 kwad...@gmail.com wrote: > *Hi SageMath Team,* > > I am *Dr. Kshipra Wadikar*, and I have a *PhD in Noncommutative Algebra*. > I am interested in contributing to SageMath’s *Lie Algebra and Quantum > Group module* for *GSoC 2025*. I have experience in *Python.* > > I have reviewed SageMath’s existing Lie algebra implementation and found > that representation theory can be extended. Below is a *short summary* of > my proposal: > > *1. Define a framework for Lie algebra representations* (modules, weight > spaces, tensor products). > 2. *Implement fundamental and irreducible representations* (Verma > modules, highest weight representations). > 3. *Develop algorithms for weight multiplicities and branching rules*. > *4. Introduce quantum groups (Drinfeld-Jimbo definition) and their > representations*. > > Would this be a *good project for SageMath*? I’d love to get *your > feedback* before submitting the full proposal. > > Thank you! > > *Best,* > Kshipra Wadikar > -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-gsoc+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sage-gsoc/386cd3e3-2e6b-49a5-927e-5f254fba7ad9n%40googlegroups.com.
