an:02211627
Zbl 1140.17015
Nakajima, Hiraku
Quiver varieties and \(t\)-analogs of \(q\)-characters of quantum affine algebras
EN
Ann. Math. (2) 160, No. 3, 1057-1097 (2005).
00117108
2005
j
17B37 33D80
Summary: We consider a specialization of an untwisted quantum affine algebra of type ADE at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of its finite dimensional representations has two bases, simple modules and standard modules. We identify entries of the transition matrix with special values of ``computable'' polynomials, similar to Kazhdan-Lusztig polynomials. At the same time we ``compute'' \(q\)-characters for all simple modules. The result is based on ''computations'' of Betti numbers of graded/cyclic quiver varieties.