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

(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). We demonstrate a promotion-and evacuation-preserving embedding of SYT (sc(k)) into SYT(k(k+1)). We hope that this result, together with results by Rhoades on rectangular tableaux, can help to demonstrate the cyclic sieving phenomenon of promotion action on SYT(sc(k)).