Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The generating rank of the unitary and symplectic Grassmannians   We prove that the Grassmannian of totally isotropic $k$-spaces of the polar
space associated to the unitary group $\mathsf{SU}_{2n}(\mathbb{F})$ ($n\in
\mathbb{N}$) has generating rank ${2n\choose k}$ when $\mathbb{F}\ne
\mathbb{F}_4$. We also reprove the main result of Blok [Blok2007], namely that
the Grassmannian of totally isotropic $k$-spaces associated to the symplectic
group $\mathsf{Sp}_{2n}(\mathbb{F})$ has generating rank ${2n\choose
k}-{2n\choose k-2}$, when $\rm{Char}(\mathbb{F})\ne 2$.

31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th