International Congress of Mathematicians

Representations of Yangians 6478 9 3 41234567-3-4-2-30-1-2For each k = 1, ..., n put Ck = j — i if the box (i, j) e a; is filled with thenumber k in the tableau 0. The difference j — i is called the content of the box(i,j) of the diagram UJ. Our choice of the tableau 0 provides an ordering of thecollection of all contents of UJ. In the above figure, on the left we show the columntableau 0 for the partitions À = (5,3,3,3,3,0,0,...) and p = (3,3,2,0,0,...). Onthe right we indicate the contents of all boxes of UJ.Introduce n complex variables ti, ... ,t n with the constraints tk = U for allk and I occuring in the same column of 0. The number of independent variablesamong ti, ... ,t n equals the number of non-empty columns in the diagram UJ. Orderlexicographically the set of all pairs (k,l) with 1 ^ k < I ^ n. Take the orderedproduct over this set,n (i -. PM \ , ) (1.9)l