On representation categories of wreath products in non-integral rank

@article{Mori2011OnRC,
  title={On representation categories of wreath products in non-integral rank},
  author={Masaki Mori},
  journal={Advances in Mathematics},
  year={2011},
  volume={231},
  pages={1-42}
}
  • M. Mori
  • Published 25 May 2011
  • Mathematics
  • Advances in Mathematics

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References

SHOWING 1-10 OF 19 REFERENCES

A construction of semisimple tensor categories

REPRESENTATION THEORY IN COMPLEX RANK, I

P. Deligne defined interpolations of the tensor category of representations of the symmetric group Sn to complex values of n. Namely, he defined tensor categories Rep(St) for any complex t. This

G-colored partition algebras as centralizer algebras of wreath products

Tensor envelopes of regular categories

Finite quantum groupoids and inclusions of finite type

Bialgebroids, separable bialgebroids, and weak Hopf algebras are compared from a categorical point of view. Then properties of weak Hopf algebras and their applications to finite index and finite

CHARACTERIZATION FOR THE MODULAR PARTY ALGEBRA

In this paper, we give a characterization for the modular party algebra Pn,r(Q) by generators and relations. By specializing the parameter Q to a positive integer k, this algebra becomes the

Note on Frobenius monoidal functors

It is well known that strong monoidal functors preserve duals. In this short note we show that a slightly weaker version of functor, which we call "Frobenius monoidal", is sufficient.

TEMPERLEY-LIEB ALGEBRAS FOR NON-PLANAR STATISTICAL MECHANICS — THE PARTITION ALGEBRA CONSTRUCTION

We give the definition of the Partition Algebra Pn(Q). This is a new generalisation of the Temperley–Lieb algebra for Q-state n-site Potts models, underpinning their transfer matrix formulation on

Young tableaux

This paper gives a qualitative description how Young tableaux can be used to perform a Clebsch-Gordan decomposition of tensor products in SU(3) and how this can be generalized to SU(N).