#####
Séminaire Lotharingien de Combinatoire, 80B.74 (2018), 12 pp.

# Ryan Kaliszewski, Justin Lambright, and Mark Skandera

# Bases of the Quantum Matrix Bialgebra and Induced Sign Characters of the Hecke Algebra

**Abstract.**
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 *H*_{n}(*q*)
at all elements of
the form (1 + *T*_{si1}) ...
(1 + *T*_{sim}),
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 *H*_{n}(*q*).

Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.

The following versions are available: