Imaginary vectors in the dual canonical basis of $U_q(n)$
| dc.creator | Leclerc, Bernard | |
| dc.date | 2002-02-15 | |
| dc.date | 2002-09-11 | |
| dc.date.accessioned | 2026-07-07T04:46:28Z | |
| dc.date.available | 2026-07-07T04:46:28Z | |
| dc.description | 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. | |
| dc.description | 11 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0202148 | |
| dc.identifier | http://arxiv.org/abs/math/0202148 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63348 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 17B 20C | |
| dc.title | Imaginary vectors in the dual canonical basis of $U_q(n)$ | |
| dc.type | text |