Level Zero Fundamental Representations over Quantized Affine Algebras and Demazure Modules

By Masaki Kashiwara. 2003

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Let W ( k) be the finite-dimensional irreducible module over a quantized affine algebra U ′ q(g) with the fundamental weight k as an extremal weight. We show that its crystal B(W ( k)) is isomorphic to the Demazure crystal B (−Λ0 + k). This is derived from the following general result: for a dominant integral weight λ and an integral weight μ, there exists a unique homomorphism U− q (g)(uλ ⊗ uμ) → V (λ+ μ) that sends uλ ⊗ uμ to uλ+μ. Here V (λ) is the extremal weight module with λ as an extremal weight, and uλ ∈ V (λ) is the extremal weight vector of weight λ. §

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9375ed292858400f9ee72f2ec2d2b31649aba50a

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Citations in the corpus

Tensor Product Structure of Affine Demazure Modules and Limit Constructions (2004, background): “For all fundamental g-weights ωi Kashiwara constructed this irreducible finite-dimensional integrable U ′q(ĝ)-module KR(ωi) and showed that it is good and even more that the crystal is isomorphic to a certain generalized Demazure crystal as a g-crystal.”
Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions (2005, background): “[26] Let g be a simple Lie algebra of simply laced type, then”