For n >= 2 consider the affine Lie algebra (sl) over cap with simple roots {alpha(i) vertical bar 0 = 1) denote the integrable highest weight (sl) over cap (n)-module with highest weight k Lambda 0. It is known that there are finitely many maximal dominant weights of V (k Lambda(0)). Using the crystal base realization of V (k Lambda(0)) and lattice path combinatorics we examine the multiplicities of a large set of maximal dominant weights of the form k Lambda(0) - lambda(l)(a,b) where lambda(l)(a,b) = l alpha(0)+(l - b)alpha(1)+(l -(b+1))alpha(2)+...+alpha(l-b) + alpha(n-l+a) +2 alpha(n-l+a+1)+...+(l-a)alpha(n-1), and k >= a + b, a, b is an element of Z(>= 1), max{a, b} <= l <= left perpendicularn+a+ bright perpendicular2 - 1. We obtain two formulae to obtain these weight multiplicities - one in terms of certain standard Young tableaux and the other in terms of certain pattern-avoiding permutations.
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