Christopher D. Long

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math.GR2026

The Mathieu Property for Compact Connected Lie Groups

Christopher D. Long

Let $G$ be a compact connected Lie group, let $R (G)$ denote its algebra of representative functions, and let $I_{G} (f) = \int_{G} f (g) d g$ be normalized Haar…

math.GR2026

Counterexamples to the xz-Conjecture and the Mathieu Conjecture for SU(2)

Christopher D. Long

Let \[ {\mathcal I}(h)=\int_0^1\int_{\mathbb T}h(x,z)\,\frac{dz}{2πiz}\,dx \qquad \bigl(h\in{\mathbb C}[x,z,z^{-1}]\bigr). \] We give the three-term Laurent polynomial \[ f(x,z)=(1…