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J. Korean Math. Soc. 2012; 49(4): 745-763

Printed July 1, 2012

https://doi.org/10.4134/JKMS.2012.49.4.745

Copyright © The Korean Mathematical Society.

Hankel Pfaffians, discriminants and Kazhdan-Lusztig bases

Alain Lascoux

Universit\'e de Paris-Est

Abstract

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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.

Keywords: Pfaffians, discriminants, Kazhdan-Lusztig bases

MSC numbers: 05E05, 05E10, 15A15, 20C30

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