Abstract
The Cartan subalgebra of the quantum loop algebra Graphic is generated by a family of mutually commuting operators, responsible for the l-weight decomposition of finite-dimensional Graphic-modules. The natural Jordan filtration induced by these operators is generically non-trivial on l-weight spaces of dimension greater than 1. We derive, for every standard module of Graphic, the dimensions of the Jordan grades and prove that they can be directly read off from the t-dependence of the q,t-characters introduced by Nakajima. To do so, we construct explicit bases for the standard modules of Graphic with respect to which the Cartan generators are upper-triangular. The basis vectors of each l-weight space are labeled by the elements of a ranked poset from the family L(m,n).
| Original language | English |
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| Pages (from-to) | 2179-2211 |
| Number of pages | 33 |
| Journal | Int. Math. Res. Notices |
| Volume | 2012 |
| Issue number | 10 |
| Early online date | 8 Jun 2011 |
| DOIs | |
| Publication status | Published - 2011 |