Imaginary vectors in the dual canonical basis of $U_q(n)$

Details Imaginary vectors in the dual canonical basis of $U_q(n)$ Imaginary vectors in the dual canonical basis of $U_q(n)$

2002-02-15

arxiv.org/abs/math/0202148v2

Mathematics

Quantum Algebra

11 pages, 5 figures

Scientific paper

Let $n$ be the maximal nilpotent subalgebra of a simple complex Lie algebra $g$. We introduce the notion of imaginary vector in the dual canonical basis of $U_q(n)$, and we give examples of such vectors for types $A_n (n\ge 5)$, $B_n (n\ge 3)$, $C_n (n\ge 3)$, $D_n (n\ge 4)$, and all exceptional types. This disproves a conjecture of Berenstein and Zelevinsky about $q$-commuting products of vectors of the dual canonical basis. It also shows the existence of finite-dimensional irreducible representations of quantum affine algebras whose tensor square is not irreducible.

Affiliated with

Also associated with

No associations

Rating

Imaginary vectors in the dual canonical basis of $U_q(n)$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Imaginary vectors in the dual canonical basis of $U_q(n)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Imaginary vectors in the dual canonical basis of $U_q(n)$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-709712