I’m in California for 11 days, for (mostly) math. Here’s something fun I just learned from Dick Gross. Let be a split simple algebraic group over , and let be (a -lattice in) an irreducible algebraic representation of . It’s not hard to check that if is minuscule, the representation is an irreducible -representation for every prime . Are there any other examples of with this property? It turns out there is exactly one more example: the adjoint representation of . When I said it was surprising to me that another such example existed, Dick explained that I shouldn’t be surprised, because after all, “ is the greatest group that God ever created, so it’s not surprising that it has amazing properties like this”.
Top Posts & Pages
arithmetica on Superfectoid spaces!? arithmetica on Superfectoid spaces!? mayorliatmath on Superfectoid spaces!? lucqin on Superfectoid spaces!? Jesse on Fun with crystalline peri…
Tagsabelian varieties Auslander automorphic forms Bellaiche Bergdall Berger Breuil-Schneider conjecture Brian Conrad Buchsbaum Buzzard Chenevier Chojecki cohomology Coleman Colmez commutative algebra completed cohomology Eichler eigenvarieties Emerton explicit things Fargues Fontaine Gauss sums Hida Huber Kedlaya Lutkebohmert modular forms Newton nonsense not p-adic Hodge theory overconvergent modular forms p-adic geometry p-adic Hodge theory p-adic Langlands p-divisible groups perfectoid things Pilloni quadratic residues Scholze Sen Shimura Shimura varieties Tate Urban Verberkmoes verma modules Weinstein zeitgeist