an:01820881
Zbl 1011.17012
Varagnolo, M.; Vasserot, E.
Standard modules of quantum affine algebras
EN
Duke Math. J. 111, No. 3, 509-533 (2002).
00089569
2002
j
17B37 16G20
quiver varieties; quantum affine algebras
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 [\textit{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 \textit{T. Akasaka} and \textit{M. Kashiwara} [Publ. Res. Inst. Math. Sci. 33, 839--867 (1997; Zbl 0915.17011)], in the case of simply laced types, is obtained.
Stefano Capparelli (Roma)
Zbl 0970.17017; Zbl 0915.17011