The hodge theory of soergel bimodules
http://people.mpim-bonn.mpg.de/geordie/papers.html WebMar 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]
The hodge theory of soergel bimodules
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WebThe Hodge theory of Soergel bimodules (with Ben Elias), Annals of Mathematics, (2) 180 (2014), no. 3, 1089-1136.. In geometric situations Soergel bimodules can be realised as the equivariant intersection cohomology of Schubert varieties, and hence have interesting real Hodge theory (hard Lefschetz, Hodge-Riemann bilinear relations etc). 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. WebSep 22, 2015 · The (two-colored) Temperley–Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable Soergel bimodules are the images of Jones–Wenzl projectors. When W is infinite, the parameter q of the Temperley–Lieb algebra may be generic, yielding a quantum version of the geometric ...
WebDec 4, 2012 · The Hodge theory of Soergel bimodules arXiv Authors: Ben Elias Geordie Williamson Abstract We prove Soergel's conjecture on the characters of indecomposable … 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 …
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-
WebUsing the diagrammatic calculus for Soergel bimodules, developed by B. Elias and M. Khovanov, as well as Rasmussen’s spectral sequence, we construct an integral version of HOMFLY-PT and -link homology. onthouden cartoonWebOct 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 ios mail multiple accountsWebThe 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 … ios mails sichernWebWe 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 … onthouding definisieWebApr 4, 2024 · We first formulate and prove a version of Premet’s conjecture for finite W-superalgebras associated with basic Lie superalgebras. As in the case of W-algebras, Premet’s conjecture is very close to giving a classification of finite-dimensional simple modules of finite W-superalgebras. In the case of basic type I Lie superalgebras, we … ios mail protect mail activityWebSep 26, 2024 · This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful … ios mail microsoft 365WebWe prove Soergel’s conjecture on the characters of indecomposable Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coefficients for arbitrary Coxeter … ios mail remove account