Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Support varieties of $(\frak g, \frak k)$-modules of finite type   Let $\frak g$ be a reductive Lie algebra over an algebraically closed field
of characteristic 0 and $\frak k$ be a reductive in $\frak g$-subalgebra. Let
$M$ be a finitely generated (possibly, infinite-dimensional) $\frak g$-module.
We say that $M$ is a $(\frak g, \frak k)$-module if $M$ is a direct sum of a
(possibly, infinite) amount of simple finite-dimensional $\frak k$-modules. We
say that $M$ is of finite type if $M$ is a $(\frak g, \frak k)$-module and
Hom$_\frak k(V, M)<\infty$ for any simple $\frak k$-module $V$.
  Let $X$ be a variety of all Borel subalgebras of $\frak g$. Let $M$ be a
finitely generated $(\frak g, \frak k)$-module of finite type. In this article
we prove that $M$ is holonomic, i.e. $M$ is governed by some subvariety
$L_M\subset X$ and some local system $S_M$ on it. Furthermore we provide a
finite list in which L$_M$ necessarily appear.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin