Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphisms of graphs corresponding to conjugacy classes of
  finite-rank self-adjoint operators   We consider the graph whose vertex set is a conjugacy class ${\mathcal C}$
consisting of finite-rank self-adjoint operators on a complex Hilbert space
$H$. The dimension of $H$ is assumed to be not less than $3$. In the case when
operators from ${\mathcal C}$ have two eigenvalues only, we obtain the
Grassmann graph formed by $k$-dimensional subspaces of $H$, where $k$ is the
smallest dimension of eigenspaces. Classical Chow's theorem describes
automorphisms of this graph for $k>1$. Under the assumption that operators from
${\mathcal C}$ have more than two eigenvalues we show that every automorphism
of the graph is induced by a unitary or anti-unitary operator up to a
permutation of eigenspaces with the same dimensions. In contrast to this
result, Chow's theorem states that there are graph automorphisms induced by
semilinear automorphisms not preserving orthogonality if ${\mathcal C}$ is
formed by operators with precisely two eigenvalues.

35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con