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i have 2 matrix representations of SU(2) . each of them uses a up> and down basis (d> and u>

If i take their tensor product i will get 4*4 matrices with this basis:

d>d>,d>u>,u>d>,u>u>

these representation is the sum equal to the sum of the 0-representation , a singlet represertation with

m= 0 and a 1-representation of 3*3 matris with m= -1,0,1

i have two states with m= 0 corresponding to u>d> and d>u> in their vector space.

if i start with m = 1 a ladder operator will decrease m to 0 that will be in the triplet .

How to write this action of the ladder operator in the 4 vector basis?