Abstract
The application of two fundamental discretizations of Weyl-orbit functions to an electron propagation on the graphene triangular dots are presented. Symmetries of the point and label sets inside dual weight and root lattices of root systems are provided by affine and extended affine Weyl groups. The discrete orthogonality relations of the Weyl-orbit functions over the dual weight and root point sets induce four types of complex discrete Fourier-Weyl transforms. Subtractively combining the transforms of the \(A_2\) group induces two types of extended Weyl-orbit functions and their corresponding discrete transforms on the fragment of the honeycomb lattice. Special types of extended Weyl-orbit functions represent stationary states of the electron propagation on the triangular graphene dot with armchair boundaries.
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