Skandera showed that all dual canonical basis elements of C[SL_m] can be written in terms of Kazhdan-Lusztig immanants, which were introduced by Rhoades and Skandera. We use this result as well as Lewis Carroll's identity (also known as the Desnanot-Jacobi identity) to show that a broad class of dual canonical basis elements are positive when evaluated on k-positive matrices, matrices whose minors of size k and smaller are positive. This is joint work with Melissa Sherman-Bennett.

Speaker(s): Sunita Chepuri (University of Michigan)