Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The harmonic transvector algebra in two vector variables   The decomposition of polynomials of one vector variable into irreducible
modules for the orthogonal group is a crucial result in harmonic analysis which
makes use of the Howe duality theorem and leads to the study of spherical
harmonics. The aim of the present paper is to describe a decomposition of
polynomials in two vector variables and to obtain projection operators on each
of the irreducible components. To do so, a particular transvector algebra will
be used as a new dual partner for the orthogonal group leading to a
generalisation of the classical Howe duality. The results are subsequently used
to obtain explicit projection operators and formulas for integration of
polynomials over the associated Stiefel manifold.

19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
16
The categories of this paper are: stat
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The categories of this paper are: nucl-ex