A tableau formula for eta polynomials

作者：Tamvakis Harry^*

来源：Mathematische Annalen, 2014, 358(3-4): 1005-1029.

DOI：10.1007/s00208-013-0982-6

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) over tilde (n) of type D-n. We define the skew elements of (W) over tilde (n) and exhibit a bijection between the set of reduced words for any skew w is an element of (W) over tilde (n) and a set of certain standard typed tableaux on a skew shape lambda/mu associated to w.

• 出版日期2014-4