Timeline for Equivariant K-theory of projective representation on complex projective space
Current License: CC BY-SA 3.0
3 events
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| Aug 30, 2016 at 22:43 | comment | added | Akhil Mathew | @GregoryArone: that sounds like a good idea. Thanks! | |
| Aug 30, 2016 at 6:13 | comment | added | Gregory Arone | A projective representation of $G$ corresponds to a linear representation of a central extension of $G$ by a circle. Let's denote it $\tilde G$. The $G$-equivariant complex $K$-theory of ${\mathbb P}(V)$ is the same as the $\tilde G$ equivariant $K$-theory of $S(V)$ (the unit sphere of $V$). If I am not confused, this is the representation ring of $\tilde G$, quotiened by the ideal generated by $V$. In your example, $\tilde G$ is the subgroup of $U(p)$ generated by the center and your $C_p\times C_p$. So now we have to calculate the representation ring of this group. Shouldn't be too hard... | |
| Aug 30, 2016 at 1:40 | history | asked | Akhil Mathew | CC BY-SA 3.0 |