*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 <tcscr...@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+unsubscr...@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/CADCaQTK%2Bk1H8aczzduLYyCfvrFBXGebBpbe%2BZZzGOzba5FVEeA%40mail.gmail.com.
