Mathematics – Representation Theory
Scientific paper
2011-01-03
Mathematics
Representation Theory
46 pages
Scientific paper
The article concerns the subalgebra U_v^+(w) of the quantized universal enveloping algebra of the complex Lie algebra sl_{n+1} associated with a particular Weyl group element of length 2n. We verify that U_v^+(w) can be endowed with the structure of a quantum cluster algebra of type A_n. The quantum cluster algebra is a deformation of the ordinary cluster algebra Geiss-Leclerc-Schroeer attached to w using the representation theory of the preprojective algebra. Furthermore, we prove that the quantum cluster variables are, up to a power of v, elements in the dual of Lusztig's canonical basis under Kashiwara's bilinear form.
No associations
LandOfFree
Quantum cluster algebras of type A and the dual canonical basis 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 Quantum cluster algebras of type A and the dual canonical basis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum cluster algebras of type A and the dual canonical basis will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-239425