Characters and blocks for finite-dimensional representations of quantum affine algebras

By Vyjayanthi Chari, A. Moura. 2004

55 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bbbb120674f649a2af44da087a54053553dc59fb

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Citations in the corpus

Quantum Geometry and Quiver Gauge Theories (2013, methodology): “Hernandez [97] constructed (q, t)-characters for gΓ-quantum affine algebra U q (gΓ) of generic symmetrizable Kac-Moody Lie algebra gΓ, developed representation theory in [134] and constructed quantum fusion tensor category in [135]; Chari et al [136, 137] constructed fundamental U q (g) q-characters”
BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, background): “The latter is familiar from the study of lattice and massive integrable field theories in two dimensions [111, 112, 115, 109, 110, 10, 53, 30, 32, 33, 31, 114, 21, 113, 39, 22, 60, 23, 38, 36, 20, 35].”
Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions (2005, background): “See for example [2], [3], [5], [7], [8], [10], [11], [12], [13], [16], [20], [21], [26], [28], [34] for different approaches and different aspects of this subject.”
Quantum toroidal algebras and their representations (2008, background): “However, one can combinatorially dene a natural ring structure [He3] (fusion product) on the Grothendieck group Rep(Uq(^)) of integrable representations in the category O. Indeed, consider [He3] a generalization of the Frenkel{Reshetikhinq-character morphism [FR2] (see also [Kn, CM , E]): for a rep”
Weyl, Demazure and fusion modules for the current algebra of sl r+1 (2006, result): “Given an integer n ∈ N, set [n]t = 1 − t n 1 − t ∈ N[t], [n]t ! = [1]t .”