註釋 We prove two results at the intersection of Lie theory and the representation theory of symmetric groups, Hecke algebras, and their generalizations. The first is a categorification of the crystal isomorphism B[superscript 1,1] --"B([lambda][subscript i]) E"B([lambda][subscript sigma (i)]). Here B([lambda][subscript i]) and B([lambda][subscript sigma (i)]) are two affine type highest weight crystals of weight [lambda][subscript i] and [lambda][subscript sigma (i)]) respectively, [sigma] is a specific map from the Dynkin indexing set I to itself, and B[superscript (1,1)] is a Kirillov-Reshetikhin crystal. We show that this crystal isomorphism is in fact the shadow of a richer module-theoretic phenomenon in the representation theory of Khovanov-Lauda-Rouquier algebras of classical affine type. Our second result identifies the center End[subscript H'](1) of Khovanov's Heisenberg category H', as the algebra of shifted symmetric functions [lambda] * of Okounkov and Olshanski, i.e. End[subscript H'](1)E"[lambda] *. This isomorphism provides us with a graphical calculus for [lambda] *. It also allows us to describe End[subscript H'](1) in terms of the transition and co-transition measure of Kerov and the noncommutative probability spaces of Biane 