Nicolas Libedinsky
Published 2009-06-30Version 1
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''.
Classification of weak Bruhat interval modules of $0$-Hecke algebras
Branching rules for Hecke Algebras of Type $D_{n}$
A new integral basis for the centre of the Hecke algebra of type A
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