Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note concerning Subsingular Vectors and Embedding Diagrams of the N=2
  Superconformal Algebras   Subsingular vectors of the N=2 superconformal algebras were discovered, and
examples given, in 1996. Shortly afterwards Semikhatov and Tipunin claimed to
have obtained a complete classification of the N=2 subsingular vectors in the
paper `The Structure of Verma Modules over the N=2 Superconformal algebra',
hep-th/9704111, published in CMP 195 (1998) 129. Surprisingly, the only
explicit examples of N=2 subsingular vectors known at that time did not fit
into their classification. All the results presented in that paper, including
the classification of subsingular vectors, were based on the following
assumptions: i) The authors claimed that there are only two different types of
submodules in N=2 Verma modules, overlooking from the very beginning
indecomposable `no-label' singular vectors, that had been discovered a few
months before, and clearly do not fit into their two types of submodules, and
ii) The authors claimed to have constructed `non-conventional' singular vectors
with the property of generating the two types of submodules maximally, i.e.
with no subsingular vectors left outside. In this note we prove that both
assumptions are incorrect. These facts also affect profoundly the results
presented in several other publications, especially the papers: `On the
Equivalence of Affine sl(2) and N=2 ....', by Semikhatov, hep-th/9702074,
`Embedding Diagrams of N=2 Verma Modules ....', by Semikhatov and Sirota,
hep-th/9712102, and `All Singular Vectors of the N=2 ....', by Semikhatov and
Tipunin, hep-th/9604176 (last revised version in September 98).

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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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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: adap-org
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin