The q-characters at roots of unity
We consider various specializations of the non-twisted quantum affine algebras at roots of unity. We define and study the q-characters of their finite-dimensional representations.
math.QA↗
arXiv subjects
Evgeny Mukhin
Publications and source records attributed to Evgeny Mukhin.
Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from math.QA/9810055 and derive some of their corollaries. In particular, we prove that the tensor product of fundamental representations is reducible if and only if at least one of the corresponding normalized R-matrices has a pole.
math.QA↗
Remarks on critical points of phase functions and norms of Bethe vectors
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.
math.RT↗