Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Standard monomial bases and geometric consequences for certain rings of
  invariants   Consider the diagonal action of $SL_n(K)$ on the affine space $X=V^{\oplus
m}\oplus (V^*)^{\oplus q}$ where $V=K^n, K$ an algebraically closed field of
arbitrary characteristic and $m,q>n$. We construct a "standard monomial" basis
for the ring of invariants $K[X]^{SL_n(K)}$. As a consequence, we deduce that
$K[X]^{SL_n(K)}$ is Cohen-Macaulay. We also present the first and second
fundamental theorems for $SL_n(K)$-actions.

36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol