45 citations · 310 across the 37 of their papers we have counts for
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Demazure Formulas for Weight Polytopes
Mark A. Walton
The characters of simple Lie algebras are naturally decomposed into lattice polytope sums. The Brion formula for those polytope sums is remarkably similar to the Weyl character for…
Weight-Lattice Discretization of Weyl-Orbit Functions
Jiří Hrivnák, Mark A. Walton
Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have als…
Adjoint affine fusion and tadpoles
Andrew Urichuk, Mark A. Walton
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable…
The Morse potential and phase-space quantum mechanics
B. Belchev, M. A. Walton
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast…
Polytope sums and Lie characters
M. A. Walton
A new application of polytope theory to Lie theory is presented. Exponential sums of convex lattice polytopes are applied to the characters of irreducible representations of simple…
su(N) tensor product multiplicities and virtual Berenstein-Zelevinsky triangles
Jorgen Rasmussen, Mark A. Walton
Information on su(N) tensor product multiplicities is neatly encoded in Berenstein-Zelevinsky triangles. Here we study a generalisation of these triangles by allowing negative as w…