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_{s_i₁}) ... (1 + T_{s_{i_m}}), 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.

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