α-Pfaffian, pfaffian point process and shifted Schur measure

✍ Scribed by Sho Matsumoto

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 374 KB
• Volume: 403
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2005.02.005

✦ Synopsis

For any complex number α and any even-size skew-symmetric matrix B, we define a generalization pf α (B) of the pfaffian pf(B) which we call the α-pfaffian. The α-pfaffian is a pfaffian analogue of the α-determinant studied in [T. Shirai and Y. Takahashi, J. Funct. Anal. 205 (2003) 414-463] and [D. Vere-Jones, Linear Algebra Appl. 111 (1988) 119-124]. 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 obtained in [S. Matsumoto, Correlation functions of the shifted Schur measure, math.CO/0312373] for the correlation function of the shifted Schur measure.