1
vote
1answer
131 views

Changing Left Comodules into Right Comodules via the Antipode, and Comodule Tensor Products

Let $H$ be a Hopf algebra, with invertible antipode, and let $(M,\Delta_M)$ and $(N,\Delta_N)$ be two left $H$-comodules. Now as we all know, we have a left $H$-comodule structure on the tensor ...
3
votes
2answers
433 views

Reference for the existence of a Shapovalov-type form on the tensor product of integrable modules

Shapovalov and Jantzen showed us how to construct a nice inner product on finite dimensional representations of a semi-simple Lie algebra, by simply giving the highest weight vector inner product 1 ...
3
votes
1answer
277 views

What is the “right” hermitian structure on tensor products of quantum group representations?

This is pretty specific, but there are some experts around. So, in Chari & Pressley, it's explained that in the standard *-structure, every irreducible, finite-dimensional representation of a ...