On blocks of Deligne's category Rep(S_t)
arXiv:0910.5695 · doi:10.1016/j.aim.2010.08.010
Abstract
Recently P. Deligne introduced the tensor category Rep(S_t) (for t not necessarily an integer) which in a certain precise sense interpolates the categories Rep(S_d) of representations of the symmetric groups S_d. In this paper we describe the blocks of Deligne's category Rep(S_t).
43 pages, final version, includes an added appendix as well as other modifications recommended by the referee
References in corpus (1)
Cited by in corpus (27)
- On Deligne's category $\uRep^{ab}(S_d)$
- A seminormal form for partition algebras
- Tensor categories: A selective guided tour
- On representation categories of wreath products in non-integral rank
- Simple commutative algebras in Deligne's categories Rep()
- Ambidextrous objects and trace functions for nonsemisimple categories
- Schur-Weyl duality for Deligne categories
- Semisimplicity and Indecomposable Objects in Interpolating Partition Categories
- Generating linear categories of partitions
- The subobject decomposition in enveloping tensor categories
- Stable characters from permutation patterns
- Decorated one-dimensional cobordisms and tensor envelopes of noncommutative recognizable power series
- The indecomposable objects in the center of Deligne's category
- Evaluating thin flat surfaces
- Schur-Weyl duality for Deligne categories II: the limit case
- Deligne categories and reduced Kronecker coefficients
- On representations of rational Cherednik algebras in complex rank
- Modified Traces on Deligne's Category Rep(S_{t})
- A new approach to the representation theory of the partition category
- Embedding Deligne's category in the Heisenberg category
- On the Monoidal Center of Deligne's Category Rep(S_t)
- Incidence strata of affine varieties with complex multiplicities
- Jellyfish partition categories
- Categorical actions and multiplicities in the Deligne category
- Classification of simple algebras in Deligne category
- Indecomposable objects in Khovanov-Sazdanovic's generalizations of Deligne's interpolation categories
- Generators for the representation rings of certain wreath products