کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6425881 | 1633845 | 2013 | 21 صفحه PDF | دانلود رایگان |

Let Dâµ(n) be the double Ringel-Hall algebra of the cyclic quiver â³(n) and let DâµÌ(n) be the modified quantum affine algebra of Dâµ(n). We will construct an integral form DâµÌ(n)Z for DâµÌ(n) such that the natural algebra homomorphism from DâµÌ(n)Z to the integral affine quantum Schur algebra is surjective. Furthermore, we will use Hall algebras to construct the integral form UZ(glÌn) of the universal enveloping algebra U(glÌn) of the loop algebra glÌn=gln(Q)âQ[t,tâ1], and prove that the natural algebra homomorphism from UZ(glÌn) to the affine Schur algebra over Z is surjective. In a subsequent paper (Fu [10]), we will use affine Schur algebras to give BLM realization of UZ(glÌn), and this enables us to give a new proof of the statements about UZ(glÌn) given in this paper.
Journal: Advances in Mathematics - Volume 243, 20 August 2013, Pages 1-21