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We show that $\frac{\Gamma(f_0,f_1,\dots,f_m)}{\Gamma(f_1,\dots,f_m)}=\infty$ for $m+1$ vectors having the properties that nonon-trivial linear combination of them belongs to $l_2(\mathbb N)$. Thisproperty is essential in the proof of the irreducibility of unitaryrepresentations of some infinite-dimensional groups.

The height of an infinite parallelotope is infinite