Timeline for Geometric interpretation of a formula for the induced character (fix point localization?)
Current License: CC BY-SA 3.0
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Apr 4, 2018 at 21:17 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Feb 5, 2018 at 16:46 | comment | added | David Ben-Zvi | The classic reference for this kind of argument is the proof of the Weyl character formula (generalizing the Frobenius formula you quote) in Atiyah-Bott, A Lefschetz Fixed Point Formula for Elliptic Complexes (aka the Woods Hole fixed point theorem), in the setting of compact groups. Since then this approach to character formulas has been vastly generalized - see e.g. Schmid-Vilonen in the setting of real reductive groups. The basic idea is a simple geometric one, ie just that a character = a trace = sum/integral over diagonal, but intersection of a graph with the diagonal gives fixed points | |
| Feb 5, 2018 at 8:17 | comment | added | Paul Broussous | How do you define the sheaf $\mathcal F$? This kind of formula does exist more broadly and are called Lefschetz trace formulas. However there are of cohomogical nature, i.e. involve the spaces $H^k (X^g , {\mathcal F})$. | |
| Feb 5, 2018 at 8:02 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Feb 4, 2018 at 23:18 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Feb 4, 2018 at 22:37 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Feb 4, 2018 at 22:32 | history | asked | Saal Hardali | CC BY-SA 3.0 |