Positivity properties in Hecke algebras of arbitrary Coxeter groups
Abstract: We explain why some generalizations of Kazhdan-Lusztig polynomials, obtained by considering a family of bases of Hecke algebras which generalize both the standard and costandard bases, have nonnegative coefficients. This was conjectured by Dyer, and proven by Dyer and Lehrer for finite Weyl groups. We also explain the nonnegativity of the corresponding "inverse" polynomials, which is obtained by considering a categorical action of the Artin group attached to the Coxeter system, constructed by Rouquier. Both results use the recent proof of Soergel's conjecture by Elias and Williamson.
Dr Thomas Gobet, The University of Sydney