Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometry of standard subspaces   A closed real subspace V of a complex Hilbert space H is called standard if V
intersects iV trivially and and V + i V is dense in H. In this note we study
several aspects of the geometry of the space Stand(H) of standard subspaces. In
particular, we show that modular conjugations define the structure of a
reflection space and that the modular automorphism groups extend this to the
structure of a dilation space. Every antiunitary representation of a graded Lie
group G leads to a morphism of dilation spaces Hom$_{gr}(R^x,G)$ to Stand(H).
Here dilation invariant geodesics (with respect to the reflection space
structure) correspond to antiunitary representations U of Aff(R) and they are
decreasing if and only if U is a positive energy representation. We also show
that the ordered symmetric spaces corresponding to euclidean Jordan algebras
have natural order embeddings into Stand(H) obtained from any antiunitary
positive energy representations of the conformal group.

25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg