The hodge theory of soergel bimodules
WebTHE HODGE THEORY OF SOERGEL BIMODULES 3 In [S2] and [S4] Soergel pointed out that the algebraic theory of Soergel bimodules can be developed for an arbitrary Coxeter system. Starting with an appropriate representation of the Coxeter group (the substitute for the Weyl group’s action on a Cartan subalgebra) one defines the monoidal cate- http://people.mpim-bonn.mpg.de/geordie/papers.html
The hodge theory of soergel bimodules
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WebTHE HODGE THEORY OF SOERGEL BIMODULES SETH SHELLEY-ABRAHAMSON Abstract. These are notes for a talk at the MIT-Northeastern Fall 2024 seminar on cat-egory Oand Soergel bimodules. This talk covers the rst three sections of the paper [EW] of Elias-Williamson with the same title and is entirely based on it. These notes contain no original … WebWe prove Soergel’s conjecture on the characters of indecomposable Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coefficients for arbitrary Coxeter …
WebWe will give an introduction to categorical representation theory, focusing on the example of Soergel bimodules, which is a categorification of the Iwahori-Hecke algebra. We will give … WebOct 19, 2016 · Ideas from Hodge theory have found important applications in representation theory. We give a survey of joint work with Ben Elias which uncovers Hodge theoretic structure in the Hecke category ("Soergel bimodules"). We also outline similarities and differences to other combinatorial Hodge theories. Submission history
WebThe Hodge theory of Soergel bimodules Statement of the results and outline of the methods. The embedding theorem, the limit argument. The absence of the weak Lefschetz theorem. Lightning introduction to IC, hypercohomology and Soergel bimodules Varieties stratified by affine spaces and the constructible derived category. Webism for Khovanov and Rozansky’s link homology theory. We show how this allows us to organize simplifications in the matrix factorizations appearing in their theory. In particular, it will put the equivalence of the original definition of Khovanov-Rozansky homology and the definition using Soergel bimodules
WebDec 4, 2012 · The Hodge theory of Soergel bimodules Ben Elias, Geordie Williamson (Submitted on 4 Dec 2012 ( v1 ), last revised 17 Feb 2014 (this version, v2)) We prove Soergel's conjecture on the characters of indecomposable Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coefficients for arbitrary Coxeter systems.
WebTHE HODGE THEORY OF SOERGEL BIMODULES 5 of any Bott-Samelson bimodule for a shorter expression. The bimodules Bx for x∈W give representatives for the isomorphism classes of all inde-composable Soergel bimodules up to shifts. The split Grothendieck group family corner coruñaWebSep 27, 2024 · The Hodge theory of Soergel bimodules (the topic of Part IV of this book) provides another proof. The paper provides a proof of the analogue of the relevant hard Lefschetz statement used by Braden and MacPherson, in the context of Soergel bimodules. It would be wonderful to have a proof entirely within the context of sheaves on moment … family corner astoria menuWebLocal Hodge theory of Soergel bimodules by Geordie Williamson University of Sydney Sydney, NSW, Australia Dedicated to Ben and Yeppie. 1. Introduction In this paper we … cooker terminal blockWebMar 1, 2024 · The Hodge theory of Soergel bimodules. Ann. of Math. (2), 180 (2014), pp. 1089-1136. CrossRef View in Scopus Google Scholar [2] T. Gobet. Twisted filtrations of Soergel bimodules and linear Rouquier complexes. J. Algebra, 484 (2024), pp. 275-309. View PDF View article View in Scopus Google Scholar [3] family corner early years allianceWebDec 4, 2012 · Even more, Soergel's conjecture, a massive theorem proved by Ben Elias and Geordie Williamson [EW14], says that when k is the field of real numbers R then b x is translated to B x . This paragraph ... cooker terminal outlet boxWebThe Hodge Theory of Soergel Bimodules This chapter is based on expanded notes of a lecture given by the authors and taken by Libby Taylor and Minh-Tam Trinh Abstract In … cooker temperature gaugeWebMar 13, 2013 · The Hodge theory of Soergel bimodules By Ben Elias and Geordie Williamson Abstract We prove Soergel’s conjecture on the characters of indecomposable Soergel … family corner fun survey