Timeline for "geometric" description of the algebra of central functions on a Lie group
Current License: CC BY-SA 3.0
15 events
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| Aug 18, 2017 at 23:37 | comment | added | LSpice | @ThomasNikolaus, it's not quite the Weyl alcove, is it? For example, for $\mathrm{SU}_2$, it's the projective line $S^1/{\pm1}$, not a unit interval. | |
| Jan 24, 2013 at 6:45 | vote | accept | Uwe Franz | ||
| Jan 23, 2013 at 23:30 | history | edited | Jim Humphreys |
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| Jan 23, 2013 at 23:27 | answer | added | Jim Humphreys | timeline score: 6 | |
| Jan 23, 2013 at 19:19 | comment | added | Thomas Nikolaus | The space is the Weyl alcoven, which is a simplex. This space is always homeomorphic to the quotient G/ad G. | |
| Jan 23, 2013 at 19:12 | answer | added | Allen Knutson | timeline score: 7 | |
| Jan 23, 2013 at 19:05 | comment | added | Yemon Choi | Sorry, I read your question too quickly and didn't pick up on what you were illustrating with your examples. I would be interested to know of a description such as you suggest! – Yemon Choi 0 secs ago | |
| Jan 23, 2013 at 18:10 | history | edited | Uwe Franz | CC BY-SA 3.0 |
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| Jan 23, 2013 at 17:13 | comment | added | Uwe Franz | processes has only one parameter. Of course we already know that this is true more generally for simple compact Lie groups, it has to be a multiple of the Laplace-Beltrami operator. | |
| Jan 23, 2013 at 17:05 | comment | added | Uwe Franz | Yes, thank you! I was hoping for a more "geometric" description of this set. Say we are interested in convolution semigroups of central probability measures (or, equivalently, conjugate invariant Levy processes). For this I have to study how I can move move away from the identity. The descriptions above for SU(2) and SU(3) show that there is only one possible direction to leave the identity without jumping (the identity is the boundary point to the right, i.e. 2 for SU(2) and (3,0) for SU(3)). This explains intuitively why the diffusion part in the generator of conjugate invariant Levy | |
| Jan 23, 2013 at 16:47 | comment | added | Yemon Choi | (For you want a cts function constant on conjugacy classes, hence by max torus theory it can be viewed as a function on T/W. Then appeal to something like Peter-Weyl in form of combinations of group characters to show that the map from your algebra to C(T/W) has dense range, so by cstar theory is onto) | |
| Jan 23, 2013 at 16:43 | comment | added | Yemon Choi | Isn't this "just" maximal torus quotiented by action of Weyl group? | |
| Jan 23, 2013 at 15:51 | history | edited | Uwe Franz | CC BY-SA 3.0 |
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| Jan 23, 2013 at 15:34 | history | edited | Uwe Franz | CC BY-SA 3.0 |
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| Jan 23, 2013 at 15:20 | history | asked | Uwe Franz | CC BY-SA 3.0 |