Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariants of symplectic and orthogonal groups acting on
  $\text{GL}(n,{\mathbb C})$-modules   Let $\text{GL}(n) = \text{GL}(n, {\mathbb C})$ denote the complex general
linear group and let $G \subset \text{GL}(n)$ be one of the classical complex
subgroups $\text{O}(n)$, $\text{SO}(n)$, and $\text{Sp}(2k)$ (in the case $n =
2k$). We take a polynomial $\text{GL}(n)$-module $W$ and consider the symmetric
algebra $S(W)$. Extending previous results for $G=\text{SL}(n)$, we develop a
method for determining the Hilbert series $H(S(W)^G, t)$ of the algebra of
invariants $S(W)^G$. Then we give explicit examples for computing $H(S(W)^G,
t)$. As a further application, we extend our method to compute also the Hilbert
series of the algebras of invariants $\Lambda(S^2 V)^G$ and $\Lambda(\Lambda^2
V)^G$, where $V = {\mathbb C}^n$ denotes the standard $GL(n)$-module.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org