Characters and Blocks for Finite-Dimensional Representations of Quantum Affine Algebras

Details Characters and Blocks for Finite-Dimensional Representations of Quantum Affine Algebras Characters and Blocks for Finite-Dimensional Representations of Quantum Affine Algebras

2004-06-08

arxiv.org/abs/math/0406151v3

Mathematics

Representation Theory

Revised version. To appear in IMRN

Scientific paper

We introduce the notion of the ell-weight lattice and the ell-root lattice adapted to the study of finite-dimensional representations of quantum affine algebras. We then study the ell-weights of the fundamental representations and show that they are invariant under the action of the associated braid group, in the case when the underlying simple Lie algebra is of classical type. As an application of this result we are able to give explicit formulas for their q-characters. An example is worked out in detail in Section 5. Finally, we describe the blocks in the category and prove that they are parametrized by the quotient of the ell-weight lattice by the ell-root lattice.

Affiliated with

Also associated with

No associations

Rating

Characters and Blocks for Finite-Dimensional Representations of Quantum Affine Algebras 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 Characters and Blocks for Finite-Dimensional Representations of Quantum Affine Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characters and Blocks for Finite-Dimensional Representations of Quantum Affine Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-719373