Combinatorial bases in quantum toroidal $\mathfrak{gl}_2$ modules
Quantum Algebra
2026-01-06 v2 Mathematical Physics
Combinatorics
math.MP
Representation Theory
Abstract
We show that many tame modules of the quantum toroidal algebra can be explicitly constructed in a purely combinatorial way using the theory of -characters. The examples include families of evaluation modules obtained from analytic continuation and automorphism twists of Verma modules of the quantum affine algebra. The combinatorial bases in the modules are labeled by colored plane partitions with various properties.
Cite
@article{arxiv.2403.16705,
title = {Combinatorial bases in quantum toroidal $\mathfrak{gl}_2$ modules},
author = {Michio Jimbo and Evgeny Mukhin},
journal= {arXiv preprint arXiv:2403.16705},
year = {2026}
}
Comments
Latex, 30 pages, 12 figures. Misprints corrected, details of the proofs added