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Nov 13, 2023 at 0:38 comment added Denis T Look up papers about orbit method of A. A. Kirillov to see how exactly geometric representation theory helps to solve algebraic questions. // Another reason: BBW theorem is only true over characteristic zero alg. closed field. There are algebraic groups over arbitrary base scheme which are often interesting to study. One can say that Margulis hyperrigidity is (in some sense) a result of geometric rep theory.
Nov 11, 2023 at 20:49 comment added user1504 It's G-equivariant algebraic geometry, so the 'point' of geometric representation theory is $[pt/G]$. </dad joke>
Nov 11, 2023 at 14:28 history edited LSpice CC BY-SA 4.0
Proofreading
Nov 11, 2023 at 14:24 comment added Sam Hopkins Take a look at this previous MO answer by David Ben-Zvi: mathoverflow.net/questions/126474/…
Nov 11, 2023 at 14:12 history asked Béla Fürdőház CC BY-SA 4.0