# 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
##### Keywords:
quiver varieties; quantum affine algebras
Full Text: