# Infinitely high* *parallelotopes

Linear algebra

We demonstrate that the height of an infinite parallelotope is infinite if no non-trivial combinations of its edges belong to $l_2(\mathbb N)$.

## The height of an infinite parallelotope is infinite

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We show that Γ(f0,f1,…,fm)Γ(f1,…,fm)=∞ for m+1 vectors having the properties that no non-trivial linear combination of them belongs to l2(ℕ). This property is essential in the proof of the irreducibility of unitary representations of some infinite-dimensional groups.

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