Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alpha-determinant cyclic modules and Jacobi polynomials   We study the cyclic $U(\mathfrak{gl}_n)$-module generated by the $l$-th power
of the $\alpha$-determinant. When $l$ is a non-negative integer, for all but
finite exceptional values of $alpha$, one shows that this cyclic module is
isomorphic to the $n$-th tensor space $(S^l(\mathbb{C}^n))^{\otimes n}$ of the
symmetric $l$-th tensor space of $\mathbb{C}^n$. If $alpha$ is exceptional,
then the structure of the module changes drastically, i.e. some irreducible
representations which are the irreducible components of the decomposition of
$(S^l(\mathbb{C}^n))^{\otimes n}$ disappear in the decomposition of the cyclic
module. The degeneration of each isotypic component of the cyclic module is
described by a matrix whose size is given by a Kostka number and entries are
polynomials in $alpha$ with rational coefficients. As a special case, we
determine the matrix in a full of the detail for the case where $n=2$; the
matrix becomes a scalar and is essentially given by the classical Jacobi
polynomial. Moreover, we prove that these polynomials are unitary.

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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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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: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: econ