Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac series of $GL(n, \mathbb{R})$   The unitary dual of $GL(n, \mathbb{R})$ was classified by Vogan in the 1980s.
Focusing on the irreducible unitary representations of $GL(n, \mathbb{R})$ with
half-integral infinitesimal characters, we find that Speh representations and
the special unipotent representations are building blocks. By looking at the
$K$-types of them, and by using a Blattner-type formula, we obtain all the
irreducible unitary $(\mathfrak{g}, K)$-modules with non-zero Dirac cohomology
of $GL(n, \mathbb{R})$, as well as a formula for (one of) their spin-lowest
$K$-types. Moreover, analogous to the $GL(n,\mathbb{C})$ case given in [DW1],
we count the number of the FS-scattered representations of $GL(n, \mathbb{R})$.

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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
28
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: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: stat