Hi Jing, Just implementing group representations as modules will not be sufficient by itself for a GSoC project. Some good additions to consider are also constructing induced/restricted representations, tensor products of representations, duals, invariants, quotients, etc. As Michael suggested, another good extension is representations of GL(n) (or other classical matrix Lie groups). Modular representation theory would also be something to consider. Do not consider this to be a comprehensive or requisite list. In my opinion, to take on this project you will likely require a solid understanding of group theory, a good understanding of algebra and representation theory is also a must. Since GSoC is primarily about coding, the majority of your time cannot be spent during the project learning the necessary background material.
Best, Travis On Thursday, March 22, 2018 at 9:40:33 AM UTC-5, Michael Walter wrote: > > Hi Jing, > > Regarding point 2, I think familiarity with the notions that are discussed > on http://doc.sagemath.org/html/en/thematic_tutorials/lie/lie_basics.html > and > http://doc.sagemath.org/html/en/thematic_tutorials/lie/weyl_character_ring.html > > would likely be a prerequisite. As a minimal requirement, a good working > knowledge of the finite-dimensional representation theory of GL(n) over the > complex numbers should be useful. > > Travis can give a more authoritative answer. > > Best, > Michael > > On Thursday, March 22, 2018 at 1:56:44 PM UTC+1, Jing Guo wrote: >> >> Hi, >> >> I am currently a sophomore majoring in CS and took honors linear algebra >> last year, where we studied linear algebra and group theory with >> application to representation theory of finite groups and disjoint >> representation of SU(2). I have used Sage to explore number theory and >> group theory. >> >> I wondered that could you help me with the following questions, since I >> could not find relevant answers on the website: >> >> 1. Did past participants usually deliver what they proposed in the >> proposal? >> 2. If I want to choose “implement group representations as modules” as my >> project, how much representation theory would it needs? >> >> Thanks. >> > -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-gsoc. For more options, visit https://groups.google.com/d/optout.
