$q$Inverting pairs of linear transformations and the $q$tetrahedron algebra
Abstract
As part of our study of the $q$tetrahedron algebra $\boxtimes_q$ we introduce the notion of a $q$inverting pair. Roughly speaking, this is a pair of invertible semisimple linear transformations on a finitedimensional 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 finitedimensional irreducible $\boxtimes_q$modules of type 1; (ii) the isomorphism classes of $q$inverting pairs.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606237
 Bibcode:
 2006math......6237I
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra;
 17B37;
 16W35 05E35;
 82B23
 EPrint:
 19 pages