×

zbMATH — the first resource for mathematics

Standard modules of quantum affine algebras. (English) Zbl 1011.17012
Let \(\mathbf U\) be the quantized enveloping algebra of \(\mathfrak{g}[t,t^{-1}]\), where \(\mathfrak{g}\) is a simple, simply laced, complex Lie algebra. A geometric realization of \(\mathbf U\) is obtained via quiver varieties [H. Nakajima, Duke Math. J. 91, 515–560 (1998; Zbl 0970.17017)]. The standard modules are a basic tool in this approach. This paper gives a construction of these modules. As a corollary, a proof of a conjecture of T. Akasaka and M. Kashiwara [Publ. Res. Inst. Math. Sci. 33, 839–867 (1997; Zbl 0915.17011)], in the case of simply laced types, is obtained.

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16G20 Representations of quivers and partially ordered sets
PDF BibTeX XML Cite
Full Text: DOI