<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-positivity of dual canonical basis elements from 1324- and 2143-avoiding Kazhdan–Lusztig immanants

In this note, we show that certain dual canonical basis elements of ℂ[SL m ] are positive when evaluated on k-positive matrices, matrices whose minors size k×k and smaller positive. Skandera showed all can be written in terms Kazhdan–Lusztig immanants, which were introduced by Rhoades Skandera. We focus the expressed immanants indexed 1324- 2143-avoiding permutations. This extends previous work authors uses similar tools, namely Lewis Carroll’s identity (also known as Desnanot-Jacobi identity).