Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp Garding inequality on compact Lie groups   In this paper the sharp Garding inequality is established on compact Lie
groups. The positivity condition is expressed in the non-commutative phase
space in terms of the full symbol, which is defined using the representations
of the group. Applications are given to the $L^2$ and Sobolev boundedness of
pseudo-differential operators.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat