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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