Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hilbert series of a linear symplectic circle quotient   We compute the Hilbert series of the graded algebra of regular functions on a
symplectic quotient of a unitary circle representation. Additionally, we
elaborate explicit formulas for the lowest coefficients of the Laurent
expansion of such a Hilbert series in terms of rational symmetric functions of
the weights. Considerable efforts are devoted to including the cases where the
weights are degenerate. We find that these Laurent expansions formally resemble
Laurent expansions of Hilbert series of graded rings of real invariants of
finite subgroups of $\U_n$. Moreover, we prove that certain Laurent
coefficients are strictly positive. Experimental observations are presented
concerning the behavior of these coefficients as well as relations among higher
coefficients, providing empirical evidence that these relations hold in
general.

23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con