Timeline for Why do combinatorists care about Kazhdan–Lusztig polynomials?
Current License: CC BY-SA 4.0
4 events
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| Aug 23 at 0:48 | comment | added | Timothy Chow | That open problem has been enough motivation for Brenti, a combinatorialist, to devote a large chunk of his career to it. This isn't motivation in the sense of "where does this come from" (to which I think the only honest answer is representation theory) but it is motivation in the sense of something that a combinatorialist can see is an interesting problem, without having to learn representation theory. | |
| Aug 23 at 0:47 | comment | added | Timothy Chow | @ChrisBowman I'm a combinatorialist myself, but my personal answer is that there isn't really any good way to motivate KL polynomials from a purely combinatorial point of view. They're interesting to combinatoralists because they have beautiful and nontrivial combinatorial properties, but that's very different from saying that they can be motivated purely combinatorially. That said, one thing you could tell the master's student is that the KL polynomials enjoy some nonnegativity properties and it is an open problem to give those numbers a combinatorial interpretation. | |
| Aug 22 at 12:48 | comment | added | Chris Bowman | Ah! But this only underscores my question! Kazhdan-Lusztig polynomials are defined entirely combinatorially. But the motivation you just cited is algebra, topology, and representation theory. These motivations require a lot of background to understand (namely, non-semisimple representation theory!) | |
| Aug 22 at 12:12 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |