Hankel Pfaffians, discriminants and Kazhdan-Lusztig bases. (English) Zbl 1244.05227
Summary: We use Kazhdan-Lusztig bases of representations of the symmetric group to express Pfaffians with entries \((a_i-a_j) h_{i+j}\). In the case where the parameters \(a_i\) are specialized to successive powers of \(q\), and the \(h_i\) are complete functions, we obtain the \(q\)-discriminant.
MSC:
05E05 | Symmetric functions and generalizations |
05E10 | Combinatorial aspects of representation theory |
15A15 | Determinants, permanents, traces, other special matrix functions |
20C30 | Representations of finite symmetric groups |