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Quiver Varieties and T-analogs of Q-characters of Quantum Affine Algebras by Nakajima, Hiraku is a scholarly article available to read on EtoBox.

What is Quiver Varieties and T-analogs of Q-characters of Quantum Affine Algebras about?

Let us 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. (The reason why we put `` '' will be explained in the end of the introduction.)

Author

Nakajima, Hiraku

Published

2001

Language

EN