Alpha-Pfaffian, pfaffian point process and shifted Schur measure
arXiv:math/0411277
Abstract
For any complex number and any even-size skew-symmetric matrix , we define a generalization $\pfaα(B)$ of the pfaffian $\pf(B)$ which we call the -pfaffian. The -pfaffian is a pfaffian analogue of the -determinant. It gives the pfaffian at . We give some formulas for -pfaffians and study the positivity. Further we define point processes determined by the -pfaffian. Also we provide a linear algebraic proof of the explicit pfaffian expression for the correlation function of the shifted Schur measure.
24 pages