We study the lifting of Schubert stratification homogeneous space complete real flags $R^{n+1}$ to its universal covering group $Spin_{n+1}$. call lifted strata Bruhat cells $Spin_{n+1}$, in keeping with homonymous classical decomposition reductive algebraic groups. present explicit parameterizations for these terms minimal-length expressions $\sigma=a_{i_1}... a_{i_k}$ permutations $\sigma\in ...

It is shown that for every p ∈ (1,∞) there exists a Banach space X of finite cotype such that the projective tensor product lp⊗̂X fails to have finite cotype. More generally, if p1, p2, p3 ∈ (1,∞) satisfy 1 p1 + 1 p2 + 1 p3 6 1 then lp1⊗̂lp2⊗̂lp3 does not have finite cotype. This is a proved via a connection to the theory of locally decodable codes.