Timeline for Character of a semisimple connected Lie groups
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 4, 2019 at 13:21 | comment | added | Jim Humphreys | An arbitrary maximal compact subgroup of a Lie group might well be reductive (almost-direct product of a semisimpe group with a compact torus) rather than semisimple. This is a drawback to using maximal compact subgrouips here. | |
| Jul 3, 2019 at 23:04 | comment | added | Ami | I'm actually not sure why would K be semisimple... | |
| Jul 3, 2019 at 17:01 | comment | added | Ami | Ok let me see if I got it, by Steinberg's lectures(page 126) there is a maximal compact subgroup K of a complex Chevalley group G, and K is Zariski-dense in G. And so the rational irreducible representations of G remain distinct and irreducible on restriction to K. K is a compact semisimple Lie group and so have no nontrivial rational characters and so does G(because different representations have different characters) am I correct? | |
| Jul 3, 2019 at 11:40 | history | edited | Jim Humphreys | CC BY-SA 4.0 |
added 36 characters in body
|
| Jul 3, 2019 at 11:34 | history | answered | Jim Humphreys | CC BY-SA 4.0 |