Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An index theorem for gauge-invariant families: The case of solvable
  groups   We define the gauge-equivariant index of a family of elliptic operators
invariant with respect to the free action of a family $\GR \to B$ of Lie groups
(these families are called ``gauge-invariant families'' in what follows). If
the fibers of $\GR \to B$ are simply-connected and solvable, we compute the
Chern character of the gauge-equivariant index, the result being given by an
Atiyah-Singer type formula that incorporates also topological information about
the bundle $\GR \to B$. The algebras of invariant pseudodifferential operators
that we study, $\Psm {\infty}Y$ and $\PsS {\infty}Y$, are generalizations of
``parameter dependent'' algebras of pseudodifferential operators (with
parameter in $\mathbb R^q$), so our results provide also an index theorem for
elliptic, parameter dependent pseudodifferential operators. We apply these
results to study Fredholm boundary conditions on a simplex.

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The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: alg-geom