Kazhdan-Lusztig Immanants for $k$-positive Matrices

Abstract: Immanants are matrix functionals that generalize the determinant. One notable family of immanants are the Kazhdan-Lusztig immanants. These immanants are indexed by permutations and are defined as sums involving Kazhdan-Lusztig polynomials specialized at $q=1$. Kazhdan-Lusztig immanants have several interesting combinatorial properties, including that they are nonnegative on totally positive matrices. We give a condition on permutations that allows us to extend this theorem to the setting of $k$-positive matrices.

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar