Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.
Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.
Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.
Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.
