Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Horizontal Distribution Relations for Special Cycles on Unitary Shimura
  Varieties: Split Case   We study the local behavior of special cycles on Shimura varieties for
$\mathbf{U}(2, 1) \times \mathbf{U}(1, 1)$ in the setting of the
Gan-Gross-Prasad conjectures at primes $\tau$ of the totally real field of
definition of the unitary spaces which are split in the corresponding totally
imaginary quadratic extension. We establish a local formula for their fields of
definition, and prove a distribution relation between the Galois and Hecke
actions on them. This complements work of \cite{jetchev:unitary} at inert
primes, where the combinatorics of the formulas are reduced to calculations on
the Bruhat--Tits trees, which in the split case must be replaced with
higher-dimensional buildings.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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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: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: gr-qc