Timeline for nil Hecke algebra and Coxeter elements
Current License: CC BY-SA 3.0
3 events
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| Nov 27, 2012 at 15:38 | comment | added | David Hill | I don't think this answers your question, so I'll leave it as a comment. In Khovanov-Lauda's paper `A diagramatic approach to categorification of quantum groups II', equations (11)-(13) give some formulas for the interaction between $T_w$, $w$ the Coxeter element, and certain idempotents acting on polynomials ($W$ is the symmetric group). These formulas are then used to prove the categorical Serre relations, which takes the form of an exact sequence. One of the maps is given by multiplying by the Coxeter element in the quiver Hecke algebra. | |
| Nov 21, 2012 at 17:44 | comment | added | Jim Humphreys | @Victor: I guess you are working in the framework of Kostant and Kumar? It would be helpful to add a background reference for the basic construction and properties such as the action on polynomials. (Also, I'm unsure why you use the term "algebra" rather than just "ring" here. In the Kostant-Kumar construction of the nil Hecke ring there is no direct use of a generic Iwahori-Hecke algebra or its various specializations.) | |
| Nov 21, 2012 at 3:21 | history | asked | Victor Ginzburg | CC BY-SA 3.0 |