Séminaire Lotharingien de Combinatoire, 84B.70 (2020), 11 pp.

Sunita Chepuri and Melissa Sherman-Bennett

123, 2143-Avoiding Kazhdan-Lusztig Immanants and k-Positive Matrices

Abstract. Immanants are functions on square matrices generalizing the determinant and permanent. Stembridge showed that irreducible character immanants are nonnegative on totally nonnegative matrices. Rhoades and Skandera later defined Kazhdan-Lusztig immanants, using specializations of Kazhdan-Lusztig polynomials at 1; results of (Stembridge, 1992) and (Haiman, 1993) show that these are also nonnegative on totally nonnegative immanants. Here, we give conditions on v in S_n so that the Kazhdan-Lusztig immanant corresponding to v is positive on k-positive matrices.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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