Fatemeh Nikzad Pasikhani
Stability Theorem for $ \mathbb{Z}_{2}^{n} $-Lie supergroups
We show that every pre-representation of a $ \mathbb{Z}_{2}^{n} $-Lie supergroup has a unique extension to a unitary representation. By a $ \mathbb{Z}_{2}^{n} $-Lie supergroup we mean a Harish-Chandra pair $ (G_0, \mathfrak{g}_{\mathbb{C}}) $ where $ G_0 $ is a common Lie Group and $ \mathfrak{g}_{\mathbb{C}} $ is a $ \mathbb{Z}_{2}^{n} $-graded Lie superalgebra such that there exists an action $Ad:G_0 \times \mathfrak{g_{\mathbb{C}}} \rightarrow \mathfrak{g_{\mathbb{C}}} $ preserves the $\mathbb{Z}_{2}^{n}$-grading and $ \mathrm{Ad}|_{\mathfrak{g_{0}}}:G_{0} \times \mathfrak{g_{0}} \rightarrow \mathfrak{g_{0}} $ is the adjoint action of $G_0$ on $\mathfrak{g_{0}} \cong Lie(G_{0})$.
