Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic extension techniques for unitary representations of Banach-Lie
  groups   Let $(G,\theta)$ be a Banach--Lie group with involutive automorphism
$\theta$, $\g = \fh \oplus \fq$ be the $\theta$-eigenspaces in the Lie algebra
$\g$ of $G$, and $H = (G^\theta)_0$ be the identity component of its group of
fixed points. An Olshanski semigroup is a semigroup $S \subeq G$ of the form $S
= H \exp(W)$, where $W$ is an open $\Ad(H)$-invariant convex cone in $\fq$ and
the polar map $H \times W \to S, (h,x) \mapsto h \exp x$ is a diffeomorphism.
Any such semigroup carries an involution * satisfying $(h\exp x)^* = (\exp x)
h^{-1}$. Our central result, generalizing the L\"uscher--Mack Theorem for
finite dimensional groups, asserts that any locally bounded *-representation
$\pi \: S \to B(\cH)$ with a dense set of smooth vectors defines by "analytic
continuation" a unitary representation of the simply connected Lie group $G_c$
with Lie algebra $ \g_c = \fh + i \fq$. We also characterize those unitary
representations of $G_c$ obtained by this construction. With similar methods,
we further show that semibounded unitary representations extend to holomorphic
representations of complex Olshanski semigroups

26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat