Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of
  5D AGT Conjecture   In this thesis, we obtain the formula for the Kac determinant of the algebra
arising from the level $N$ representation of the Ding-Iohara-Miki algebra. This
formula can be proved by decomposing the level $N$ representation into the
deformed $W$-algebra part and the $U(1)$ boson part, and using the screening
currents of the deformed $W$-algebra. It is also discovered that singular
vectors obtained by its screening currents correspond to the generalized
Macdonald functions. Moreover, we investigate the $q \rightarrow 0$ limit of
five-dimensional AGT correspondence. In this limit, the simplest 5D AGT
conjecture is proved, that is, the inner product of the Whittaker vector of the
deformed Virasoro algebra coincides with the partition function of the 5D pure
gauge theory. Furthermore, the R-Matrix of the Ding-Iohara-Miki algebra is
explicitly calculated, and its general expression in terms of the generalized
Macdonald functions is conjectured.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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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: eess
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con