Abstract
Let Vbe the standard two-dimensional representation of the algebraic group G = SL(2, C), and write V n = Sym n Vfor the irreducible (n + 1)-dimensional representation of Gon the nth symmetric tensor power of V. Also consider the (2 n )-dimensional space W n = V ⊗n , obtained as the nth tensor power of V. It is known that each V n can be written in terms of W 0,…, W n as V n = W n − W n−2 + W n−4 −…, where we view V n and the W i as virtual representations of G. We explain this phenomenon by writing down an exact sequence that gives a “resolution” of V n in terms of W 0,…, W n .
Dedicated in memory of my colleague Ahmad Shamsuddin.
Acknowledgments
Notes
Dedicated in memory of my colleague Ahmad Shamsuddin.