Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knot invariants and higher representation theory   We construct knot invariants categorifying the quantum knot variants for all
representations of quantum groups. We show that these invariants coincide with
previous invariants defined by Khovanov for sl_2 and sl_3 and by
Mazorchuk-Stroppel and Sussan for sl_n.
  Our technique is to study 2-representations of 2-quantum groups (in the sense
of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible
representations. These are the representation categories of certain finite
dimensional algebras with an explicit diagrammatic presentation, generalizing
the cyclotomic quotient of the KLR algebra. When the Lie algebra under
consideration is $\mathfrak{sl}_n$, we show that these categories agree with
certain subcategories of parabolic category O for gl_k.
  We also investigate the finer structure of these categories: they are
standardly stratified and satisfy a double centralizer property with respect to
their self-dual modules. The standard modules of the stratification play an
important role as test objects for functors, as Vermas do in more classical
representation theory.
  The existence of these representations has consequences for the structure of
previously studied categorifications. It allows us to prove the non-degeneracy
of Khovanov and Lauda's 2-category (that its Hom spaces have the expected
dimension) in all symmetrizable types, and that the cyclotomic quiver Hecke
algebras are symmetric Frobenius.
  In work of Reshetikhin and Turaev, the braiding and (co)evaluation maps
between representations of quantum groups are used to define polynomial knot
invariants. We show that the categorifications of tensor products are related
by functors categorifying these maps, which allow the construction of bigraded
knot homologies whose graded Euler characteristics are the original polynomial
knot invariants.

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat