Séminaire Lotharingien de Combinatoire, 82B.42 (2019), 12 pp.

Adam Clearwater and Mark Skandera

Total nonnegativity and evaluations of Hecke algebra characters

Abstract. Let S_[i,j] be the subgroup of the symmetric group S_n generated by adjacent transpositions (i,i+1), ..., (j-1,j). We give a combinatorial rule for evaluating induced sign characters of the type A Hecke algebra H_n(q) at all elements of the form Σ_{w in S_[i,j]} T_w and at all products of such elements. By a result of Stembridge, our result connects H_n(q) trace evaluation to immanants of totally nonnegative matrices.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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