UC Riverside

In this paper, we study the multiplicities of a level (l+1)--Demazure flag of a level l--Demazure module for the current algebra sl2[t]. We establish a recursion of the graded multiplicities and explicitly calculate these multiplicities when l=1,2. Taking the specialization q=1 of the graded multiplicity (i.e. numerical multiplicity), we establish a new recursion of polynomials related to the numerical multiplicities. We give a solution for these polynomials in two ways: as solutions of matrix equations and as coefficients in the series expansion of rational functions.