t-Analogs of q-Characters of Quantum Affine Algebras of Type E6, E7, E8
By H. Nakajima. 2006
57 citations recorded by the source corpus.
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. (Here l- stands for the loop.) In particular, we prove the fermionic formula for Kirillov–Reshetikhin modules conjectured by Hatayama et al.[Remarks on fermionic formula (1999)] for these classes of representations. We also give explicitly the monomial realization of the crystal of the corresponding fundamental representations of the quantum 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 subvarieties of quiver varieties of types E 6, E 7, E 8, respectively.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b4b172a446ebae1072b1735a2894b11a0ecad107
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Citations in the corpus
- BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, methodology): “It would be interesting to develop some kind of deformation quantization scheme, allowing to compute our qq-characters using the knowledge of the t-deformed q-characters [80], and to apply them to rederive the results of [17].”