Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An orbit model for the spectra of nilpotent Gelfand pairs   Let $N$ be a connected and simply connected nilpotent Lie group, and let $K$
be a subgroup of the automorphism group of $N$. We say that the pair $(K,N)$ is
a nilpotent Gelfand pair if $L^1_K(N)$ is an abelian algebra under convolution.
In this document we establish a geometric model for the Gelfand spectra of
nilpotent Gelfand pairs $(K,N)$ where the $K$-orbits in the center of $N$ have
a one-parameter cross section and satisfy a certain non-degeneracy condition.
More specifically, we show that the one-to-one correspondence between the set
$\Delta(K,N)$ of bounded $K$-spherical functions on $N$ and the set
$\mathcal{A}(K,N)$ of $K$-orbits in the dual $\mathfrak{n}^*$ of the Lie
algebra for $N$ established by Benson and Ratcliff is a homeomorphism for this
class of nilpotent Gelfand pairs. This result had previously been shown for $N$
a free group and $N$ a Heisenberg group, and was conjectured to hold for all
nilpotent Gelfand pairs.

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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph