Promotion and evacuation on standard Young tableaux of rectangle and staircase shape

Abstract

(Dual-)promotion and (dual-)evacuation are bijections on SYT(\lambda) for any partition \lambda. Let c^r denote the rectangular partition (c,...,c) of height r, and let sc_k (k > 2) denote the staircase partition (k,k-1,...,1). B. Rhoades showed representation-theoretically that promotion on SYT(c^r) exhibits the cyclic sieving phenomenon (CSP). In this paper, we demonstrate a promotion- and evacuation-preserving embedding of SYT(sc_k) into SYT(k^{k+1}). This arose from an attempt to demonstrate the CSP of promotion action on SYT(sc_k).