Timeline for Kapranov's analogies
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Nov 22, 2009 at 19:11 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
linkifying, mdashes
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| Nov 22, 2009 at 18:03 | comment | added | David Ben-Zvi | Yes.. the original Hall algebra of symmetric functions is directly related to Hecke operators for curves. The Ringel-Lusztig-Nakajima etc theory of Hall algebras for quivers relates to (the simplest) Hecke operators for surfaces. The new developments have to do with Calabi-Yau threefolds, which for special choices reduces to all of the above examples. One really gets a feeling from these latest developments (in particular K-S arXiv:0811.2435) of a new kind of representation theory, which specializes to the classical theory.. the physics of M5 branes gives the same feeling. exciting times! | |
| Nov 22, 2009 at 17:39 | comment | added | Thomas Riepe | Many thanks for your thought-provoking (and reading-provoking) answer! Is the representation theory of Hall algebras you mention that of Ringel? | |
| Nov 22, 2009 at 17:34 | vote | accept | Thomas Riepe | ||
| Nov 22, 2009 at 17:02 | history | answered | David Ben-Zvi | CC BY-SA 2.5 |