$t$--analogs of $q$--characters of quantum affine algebras of type $E_6$, $E_7$, $E_8$

Details $t$--analogs of $q$--characters of quantum affine algebras of type $E_6$, $E_7$, $E_8$ $t$--analogs of $q$--characters of quantum affine algebras of type $E_6$, $E_7$, $E_8$

2006-06-26

arxiv.org/abs/math/0606637v1

Representation Theory of Algebraic Groups and Quantum Groups, Progress in Mathematics, Vol. 284, 2011, 257--272

Mathematics

Quantum Algebra

13 pages, 4 tables

Scientific paper

We compute $t$--analogs of $q$--characters of all $l$--fundamental representations of the quantum affine algebras of type $E_6^{(1)}$, $E_7^{(1)}$, $E_8^{(1)}$ by a supercomputer. In particular, we prove the fermionic formula for Kirillov-Reshetikhin modules conjectured by Hatayama et al. (math.QA/9812022) for these classes of representations. We also give explicitly the monomial realization of the crystal of the corresponding fundamental representations of the qunatum enveloping algebras associated with finite dimensional Lie algebras of types $E_6$, $E_7$, $E_8$. These are computations of Betti numbers of graded quiver varieties, quiver varieties and determination of all irreducible components of the lagrangian subvarities of quiver varieties of types $E_6$, $E_7$, $E_8$ respectively.

Affiliated with

Also associated with

No associations

Rating

$t$--analogs of $q$--characters of quantum affine algebras of type $E_6$, $E_7$, $E_8$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with $t$--analogs of $q$--characters of quantum affine algebras of type $E_6$, $E_7$, $E_8$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $t$--analogs of $q$--characters of quantum affine algebras of type $E_6$, $E_7$, $E_8$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-400250