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Original Articles

A tridiagonal linear map with respect to eigenbases of equitable basis of sl2

Pages 1458-1467 | Received 18 Dec 2013, Accepted 17 Jul 2014, Published online: 14 Aug 2014
 

Abstract

Let denote an algebraically closed field, and let x, y, z be the equitable generators of over . Let V denote a finite-dimensional irreducible -module, let be a linear map. We show that if any two of the matrices representing with respect to a standard x-, y- and z-eigenbasis are tridiagonal, then acts as a linear combination of 1, x, y, z, xy, zx, yz and yzx.

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