Group representations constructions

This lecture covers the construction of representations of groups, starting with the dual representation and then exploring new representations obtained through direct sum, tensor product, dual representation, symmetric power, exterior power, sub representations, and quotient representations. The instructor also provides an example using the standard representation of sr2 on c2, illustrating the concepts discussed. Additionally, the lecture introduces the concept of a g module, symmetric power of a g module, direct sum of a g module, g invariant homomorphisms, and the category of g modules.