A tableau formula for eta polynomials

We use the Pieri and Giambelli formulas of Buch et al. (Invent Math 178:345–405, 2009 ; J Reine Angew, 2013 ) and the calculus of raising operators developed in Buch et al. (A Giambelli formula for isotropic Grassmannians, arXiv:0811.2781, 2008 ) and Tamvakis (J Reine Angew Math 652, 207–244, 2011 ) to prove a tableau formula for the eta polynomials of Buch et al. (J Reine Angew, 2013 ) and the Stanley symmetric functions which correspond to Grassmannian elements of the Weyl group W_n of type D_n . We define the skew elements of W_n and exhibit a bijection between the set of reduced words for any skew w∈W_n and a set of certain standard typed tableaux on a skew shape λ /μ associated to w .