New bases of some Hecke algebras via Soergel bimodules

Details New bases of some Hecke algebras via Soergel bimodules New bases of some Hecke algebras via Soergel bimodules

2009-06-30

arxiv.org/abs/0907.0031v1

Mathematics

Representation Theory

25 pages

Scientific paper

For extra-large Coxeter systems (m(s,r)>3), we construct a natural and explicit set of Soergel bimodules D={D_w}_{w\in W} such that each D_w contains as a direct summand (or is equal to) the indecomposable Soergel bimodule B_w. When decategorified, we prove that D gives rise to a set {d_w}_{w\in W} that is actually a basis of the Hecke algebra. This basis is close to the Kazhdan-Lusztig basis and satisfies a ``positivity condition''.

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