Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation theory of the $\alpha$-determinant and zonal spherical
  functions   We prove that the multiplicity of each irreducible component in the
$\mathcal{U}(\mathfrak{gl}_n)$-cyclic module generated by the $l$-th power
$\det^{(\alpha)}(X)^l$ of the $\alpha$-determinant is given by the rank of a
matrix whose entries are given by a variation of the spherical Fourier
transformation for $(\mathfrak{S}_{nl},\mathfrak{S}_l^n)$. Further, we
calculate the matrix explicitly when $n=2$. This gives not only another proof
of the result by Kimoto-Matsumoto-Wakayama (2007) but also a new aspect of the
representation theory of the $\alpha$-determinants.

13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ