A Scaling Limit for t-Schur Measures

To each partition λ, we introduce a measure Sλ(x; t)sλ(y)/Zt where sλ is the Schur function and Sλ(x; t) is a generalization of the Schur function defined in [M] and Zt is a normalization constant. This measure, which we call the t-Schur measure, is a generalization of the Schur measure [O] and the shifted Schur measure studied by Tracy and Widom [TW3]. We prove that by a certain specialization, a limit law for t-Schur measures is given by the Tracy-Widom distribution i.e. the limit distribution of the largest eigenvalue suitably centered and normalized in GUE.