Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Action of overalgebra in Plancherel decomposition and shift operators in
  imaginary direction   Consider the Plancherel decomposition of the tensor product of a highest
weight and a lowest weight unitary representations of $SL_2$.
  We construct explicitly the action of the Lie algebra $sl_2 + sl_2$ in the
direct integral of Hilbert spaces. It turns out that a Lie algebra operator is
a second order differential operator in one variable and second order
difference operator with respect to another variable. The difference operators
are defined in terms of the shift in the imaginary direction $f(s)\mapsto
f(s+i)$, $i^2=-1$ (the Plancherel measure is supported by real $s$).

7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc