$q$-Inverting pairs of linear transformations and the $q$-tetrahedron algebra
Representation Theory
2007-05-23 v1 Quantum Algebra
Abstract
As part of our study of the -tetrahedron algebra we introduce the notion of a -inverting pair. Roughly speaking, this is a pair of invertible semisimple linear transformations on a finite-dimensional vector space, each of which acts on the eigenspaces of the other according to a certain rule. Our main result is a bijection between the following two sets: (i) the isomorphism classes of finite-dimensional irreducible -modules of type 1; (ii) the isomorphism classes of -inverting pairs.
Keywords
Cite
@article{arxiv.math/0606237,
title = {$q$-Inverting pairs of linear transformations and the $q$-tetrahedron algebra},
author = {Tatsuro Ito and Paul Terwilliger},
journal= {arXiv preprint arXiv:math/0606237},
year = {2007}
}
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19 pages