Geodesic
Bases of the Quantum Matrix Bialgebra and Induced Sign Characters of the Hecke Algebra
Séminaire lotharingien de combinatoire, 80B (2018)

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We combinatorially describe the transition matrices which relate monomial bases of the zero-weight space of the quantum matrix bialgebra. This description leads to a combinatorial rule for evaluating induced sign characters of the (type A) Hecke algebra Hn(q) at all elements of the form (1 + Tsi1) ... (1 + Tsim), including the Kazhdan-Lusztig basis elements indexed by 321-hexagon-avoiding permutations. This result is the first subtraction-free rule for evaluating any character at all elements of a basis of Hn(q). 

@article{SLC_2018_80B_a73,
     author = {Ryan Kaliszewski and Justin Lambright, and Mark Skandera},
     title = {Bases of the {Quantum} {Matrix} {Bialgebra} and {Induced} {Sign} {Characters} of the {Hecke} {Algebra}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a73/}
}
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Ryan Kaliszewski; Justin Lambright,; Mark Skandera. Bases of the Quantum Matrix Bialgebra and Induced Sign Characters of the Hecke Algebra. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a73/