Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the principal symbols of $K_{\mathbb C}$-invariant differential
  operators on Hermitian symmetric spaces   Let $(G,K)$ be one of the following classical irreducible Hermitian symmetric
pairs of noncompact type: $(SU(p,q), S(U(p) \times U(q))),(Sp(n,R), U(n))$, or
$(SO*(2n), U(n))$. Let $G_{\mathbb C}$ and $K_{\mathbb C}$ be complexifications
of $G$ and $K$, respectively, and let $P$ be a maximal parabolic subgroup of
$G_{\mathbb C}$ whose Levi subgroup is $K_{\mathbb C}$. Let $V$ be the
holomorphic part of the complexifiaction of the tangent space at the origin of
$G/K$. It is well known that the ring of $K_{\mathbb C}$-invariant differential
operators on $V$ has a generating system $\{\varGamma_k \}$ given in terms of
determinant or Pfaffian that plays an essential role in the Capelli identities.
Our main result of this paper is that determinant or Pfaffian of the ``moment
map'' on the holomorphic cotangent bundle of $G_{\mathbb C}/P$ provides a
generating function for the principal symbols of $\varGamma_k$'s.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga