arXiv subjects
Publications and source records attributed to Nafie Tairi.
We prove that the infinite half-spin representations are topologically Noetherian with respect to the infinite spin group. As a consequence we obtain that half-spin varieties, which we introduce, are defined by the pullback of equations at a finite level. The main example for such varieties is the infinite isotropic Grassmannian in its spinor embedding, for which we explicitly determine its defining equations.
The isotropic Grassmannian parametrizes isotropic subspaces of a vector space equipped with a quadratic form. In this paper, we show that any maximal isotropic Grassmannian in its Plücker embedding can be defined by pulling back the equations of $Gr_{\operatorname{iso}}(3,7)$ or $Gr_{\operatorname{iso}}(4,8)$.
A function $f$ from $\mathbb{Z}$ to the symmetric matrices over an arbitrary field $K$ of characteristic $0$ is a $1$-quasihomomorphism if the matrix $f(x+y) - f(x) - f(y)$ has rank at most $1$ for all $x,y \in \mathbb{Z}$. We show that any such $1$-quasihomomorphism has distance at most $2$ from an actual group homomorphism. This gives a positive answer to a special case of a problem posed by Kazhdan and Ziegler.
A function $f: \mathbb{Z} \to \mathbb{Q}^n$ is a $c$-quasihomomorphism if the Hamming distance between $f(x+y)$ and $f(x)+f(y)$ is at most $c$ for all $x,y \in \mathbb{Z}$. We show that any $c$-quasihomomorphism has distance at most some constant $C(c)$ to an actual group homomorphism; here $C(c)$ depends only on $c$ and not on $n$ or $f$. This gives a positive answer to a special case of a question posed by Kazhdan and Ziegler.