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In 1998 Victor Kac classified infinite-dimensional $\mathbb{Z}$-graded Lie superalgebras of finite depth. We construct new examples of infinite-dimensional Lie superalgebras with a $\mathbb{Z}$-gradation of infinite depth and finite growth and classify $\mathbb{Z}$-graded Lie superalgebras of infinite depth and finite growth under suitable hypotheses.

In this paper we study the irreducible finite dimensional representations of the quantized enveloping algebra ${\mathcal{U}}_q\left(g\right)$ associated to $g=sl\left(3\right)$, at the roots of unity. It is known that these representations are parametrized, up to isomorphisms, by the conjugacy classes of the group $G=SL\left(3\right)$. We get a complete classification of the representations corresponding to the submaximal unipotent conjugacy class and therefore a proof of the De Concini-Kac conjecture about the dimension of the ${\mathcal{U}}_q\left(g\right)$-modules at the roots of $1$ in the...