2025/05/26 by Cao, George
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2505.19460
The distinguished weights form a subset of the weight lattice and are closely tied to the notion of p-cells. These weights are defined via iterations of the Lusztig-Vogan bijection. We prove that all distinguished weights exhibit an anti-symmetry under the composition of reversal and negation. We show that the distribution of these weights follows a polynomial asymptotic, with a leading coefficient relating to the telephone numbers. As an explicit computation, we determine all the distinguished weights for n ≤ 4.