Dear Kshipra, This could work, but it will be highly dependent on the details. The general statements are still fairly far from a good proposal. Also, let me say a bit more clearly that these wrappers to QuaGroup are already in SageMath as I recall.
Best, Travis On Tuesday, April 1, 2025 at 2:48:04 PM UTC+9 kwad...@gmail.com wrote: > *Dear SageMath Team,* > > Thank you for your detailed feedback on my initial proposal. Based on > your suggestions, I am refining my focus to address key areas that would > improve SageMath’s existing implementation, particularly in performance, > structure, and integration with GAP. > * Enhancing Integration with GAP’s QuaGroup * > > *Goal:* Improve SageMath’s interface with GAP’s QuaGroup package for > quantum groups. > 🔹 Implement wrappers in SageMath for defining quantum groups, computing > irreducible representations, and tensor product decompositions. > 🔹 Optimize performance and reduce redundancy in existing implementations. > 🔹 Improve documentation to make these tools more accessible to users. > * Parabolic Verma Modules & Morphisms* > > *Goal:* Extend SageMath’s current Verma module implementation to support > parabolic Verma modules. > 🔹 Define the structure of parabolic Verma modules in SageMath. > 🔹 Implement morphisms between Verma modules. > 🔹 Optimize computation efficiency (as current Verma modules are slow). > > Would this be a good direction for SageMath? I’d love to hear your > feedback before submitting the full proposal. > > Best regards, > *Kshipra Wadikar* > > On Mon, Mar 31, 2025 at 6:27 PM tcscrims <tcsc...@gmail.com> wrote: > >> 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+...@googlegroups.com. >> To view this discussion visit >> https://groups.google.com/d/msgid/sage-gsoc/386cd3e3-2e6b-49a5-927e-5f254fba7ad9n%40googlegroups.com >> >> <https://groups.google.com/d/msgid/sage-gsoc/386cd3e3-2e6b-49a5-927e-5f254fba7ad9n%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- 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/effc7509-2301-434c-8cb0-71fcbf6e386dn%40googlegroups.com.
