Level Zero Fundamental Representations over Quantized Affne Algebras and Demazure Modules

  • Masaki Kashiwara

    Kyoto University, Japan

Abstract

Let be the finite-dimensional irreducible module over a quantized affne algebra with the fundamental weight as an extremal weight. We show that its crystal is isomorphic to the Demazure crystal . This is derived from the following general result: for a dominant integral weight and an integral weight , there exists a unique homomorphism that sends to . Here is the extremal weight module with as an extremal weight, and is the extremal weight vector of weight .

Cite this article

Masaki Kashiwara, Level Zero Fundamental Representations over Quantized Affne Algebras and Demazure Modules. Publ. Res. Inst. Math. Sci. 41 (2005), no. 1, pp. 223–250

DOI 10.2977/PRIMS/1145475409