Evgeny Mukhin, Alexander Varchenko
Published 1998-10-14Version 1
We consider a tensor product of a Verma module and the linear representation of $sl(n+1)$. We prove that the corresponding phase function, which is used in the solutions of the KZ equation with values in the tensor product, has a unique critical point and show that the Hessian of the logarithm of the phase function at this critical point equals the Shapovalov norm of the corresponding Bethe vector.
Pieri type rules and $Gl(2|2)$ tensor products
Categorifying the tensor product of a level 1 highest weight and perfect crystal in type A
Tensor products and intertwining operators for uniserial representations of the Lie algebra $\mathfrak{sl}(2)\ltimes V(m)$
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