1 November 2011 The geometry of Markov traces
Ben Webster, Geordie Williamson
Duke Math. J. 160(2): 401-419 (1 November 2011). DOI: 10.1215/00127094-1444268


We give a geometric interpretation of the Jones-Ocneanu trace on the Hecke algebra using the equivariant cohomology of sheaves on SLn. This construction makes sense for all simple groups, so we obtain a generalization of the Jones-Ocneanu trace to Hecke algebras of other types. We give a geometric expansion of this trace in terms of the irreducible characters of the Hecke algebra and conclude that it agrees with a trace defined independently by Gomi.

Based on our proof, we also prove that certain simple perverse sheaves on a reductive algebraic group G are equivariantly formal for the conjugation action of a Borel B, or equivalently, that the Hochschild homology of any Soergel bimodule is free, as the authors had previously conjectured.

This construction is also closely tied to knot homology. This interpretation of the Jones-Ocneanu trace is a more elementary manifestation of the geometric construction of HOMFLYPT homology given by the authors.


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Ben Webster. Geordie Williamson. "The geometry of Markov traces." Duke Math. J. 160 (2) 401 - 419, 1 November 2011. https://doi.org/10.1215/00127094-1444268


Published: 1 November 2011
First available in Project Euclid: 27 October 2011

zbMATH: 1254.20009
MathSciNet: MR2852120
Digital Object Identifier: 10.1215/00127094-1444268

Primary: 20C08
Secondary: 14F10 , 16T99 , 20G40

Rights: Copyright © 2011 Duke University Press


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Vol.160 • No. 2 • 1 November 2011
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