Hankel Pfaffians, discriminants and Kazhdan-Lusztig bases

DOI10.4134/JKMS.2012.49.4.745zbMATH Open1244.05227arXiv1103.4971OpenAlexW2962708637MaRDI QIDQ2898896

Alain Lascoux

Publication date: 12 July 2012

Published in: Journal of the Korean Mathematical Society (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1103.4971

zbMATH Keywords

Kazhdan-Lusztig basesdiscriminantsPfaffians

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Determinants, permanents, traces, other special matrix functions (15A15) Representations of finite symmetric groups (20C30)

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