9,382 research outputs found
Local Hodge theory of Soergel bimodules
We prove the local hard Lefschetz theorem and local Hodge-Riemann bilinear
relations for Soergel bimodules. Using results of Soergel and K\"ubel one may
deduce an algebraic proof of the Jantzen conjectures. We observe that the
Jantzen filtration may depend on the choice of non-dominant regular deformation
direction.Comment: 54 pages, v3: further minor changes. Final version to appear in Acta.
Mat
The Hodge theory of Soergel bimodules
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. Using results of Soergel one may
deduce an algebraic proof of the Kazhdan-Lusztig conjecture.Comment: 44 pages. v2: many minor changes, final versio
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