Alpha-Pfaffian, pfaffian point process and shifted Schur measure

2004/11/30 by Sho Matsumoto
Mathematics · #math.CO #math.PR #msc:15A15 #msc:05E05

paper · pdf

published as Linear Algebra and its Applications 403 (2005) 369--398 · 24 pages

arxiv created 2005/02/15 · arxiv updated 2009/12/01

Abstract

For any complex number α and any even-size skew-symmetric matrix B, we define a generalization \pfaα(B) of the pfaffian \pf(B) which we call the α-pfaffian. The α-pfaffian is a pfaffian analogue of the α-determinant. It gives the pfaffian at α=-1. We give some formulas for α-pfaffians and study the positivity. Further we define point processes determined by the α-pfaffian. Also we provide a linear algebraic proof of the explicit pfaffian expression for the correlation function of the shifted Schur measure.

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