Let Vbe the standard two-dimensional representation of the algebraic group G = SL(2, C), and write V_n = SymⁿVfor the irreducible (n + 1)-dimensional representation of Gon the nth symmetric tensor power of V. Also consider the (2ⁿ)-dimensional space W_n = V^⊗n, obtained as the nth tensor power of V. It is known that each V_ncan be written in terms of W₀,…, W_nas V_n = W_n - W_n-2 + W_n-4 -…, where we view V_nand the W_ias virtual representations of G. We explain this phenomenon by writing down an exact sequence that gives a “resolution” of V_nin terms of W₀,…, W_n.