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Let $G=KAN$ be an Iwasawa decomposition of a connected semisimple Lie group with finite center. Let us assume for simplicity that the associated symmetric space $G/K$ has rank 1. Harish-Chandras ...

Consider the Laplace operator $\Delta = d^{*} d + d d^{*}$ on $\Omega^2(S^3)$. What is the minimal eigenvalue of $\Delta$? (My computations showed that the answer is 4; the eigenforms correspond to ...