Abstract
We give a brief introduction to the theory of sheaves on moment graphs. This theory is due to Braden–MacPherson and Fiebig. It provides a very useful “local” perspective on Soergel bimodules. Our aim is a brief introduction, as well as the discussion of a few interesting examples.
This chapter is based on expanded notes of a lecture given by the authors and taken by Geordie Williamson
G. Williamson School of Mathematics and Statistics, University of Sydney, Sydney, Australia
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Notes
- 1.
This exercise explains part of the title of this subsection. At least for the author it is very useful to think of ΓyM as a “stalk” of M.
- 2.
And perhaps deceptively simple…
References
T. Braden, R. MacPherson, From moment graphs to intersection cohomology. Math. Ann. 321(3), 533–551 (2001). https://doi.org/10.1007/s002080100232
P. Fiebig, The combinatorics of Coxeter categories. Trans. Am. Math. Soc. 360(8), 4211–4233 (2008). https://doi.org/10.1090/S0002-9947-08-04376-6
P. Fiebig, G. Williamson, Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties. Ann. Inst. Fourier (Grenoble) 64(2), 489–536 (2014). http://aif.cedram.org/item?id=AIF_2014__64_2_ 489_0
J.E. Humphreys, Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics, vol. 29 (Cambridge University Press, Cambridge, 1990), pp. xii+204. https://doi.org/10.1017/CBO9780511623646
J.C. Jantzen, Moment graphs and representations, in Geometric Methods in Representation Theory. I, vol. 24. Sémin. Congr. Soc. Math. France, Paris (2012), pp. 249–341
G. Williamson, Singular Soergel bimodules. PhD thesis. Albert-Ludwigs-Universität Freiburg, 2008
G. Williamson, Local Hodge theory of Soergel bimodules. Acta Math. 217(2), 341–404 (2016). https://doi.org/10.1007/s11511-017-0146-8
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Elias, B., Makisumi, S., Thiel, U., Williamson, G. (2020). Sheaves on Moment Graphs. In: Introduction to Soergel Bimodules. RSME Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-48826-0_6
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DOI: https://doi.org/10.1007/978-3-030-48826-0_6
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