## 8 Citations

### Stability and periodicity in the modular representation theory of symmetric groups

- Mathematics
- 2015

We study asymptotic properties of the modular representation theory of symmetric groups and investigate modular analogs of stabilization phenomena in characteristic zero. The main results are…

### The indecomposable objects in the center of Deligne's category $Rep(S_t)$

- Mathematics
- 2021

We classify the indecomposable objects in the monoidal center of Deligne’s interpolation category RepSt by viewing RepSt as a model-theoretic limit in rank and characteristic. We further prove that…

### Heisenberg Categorification and Wreath Deligne Category

- Mathematics
- 2020

We define a faithful linear monoidal functor from the partition category, and hence from Deligne’s category Rep(St), to the additive Karoubi envelope of the Heisenberg category. We show that the…

### Group partition categories

- MathematicsJournal of Combinatorial Algebra
- 2021

To every group $G$ we associate a linear monoidal category $\mathcal{P}\mathit{ar}(G)$ that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient…

### The Structure of the Grothendieck Rings of Wreath Product Deligne Categories and their Generalisations

- MathematicsInternational Mathematics Research Notices
- 2019

Given a tensor category $\mathcal{C}$ over an algebraically closed field of characteristic zero, we may form the wreath product category $\mathcal{W}_n(\mathcal{C})$. It was shown in [10] that the…

### Stable Grothendieck rings of wreath product categories

- MathematicsJournal of Algebraic Combinatorics
- 2018

Let k be an algebraically closed field of characteristic zero, and let $${\mathcal {C}} = {\mathcal {R}} -\hbox {mod}$$C=R-mod be the category of finite-dimensional modules over a fixed Hopf algebra…

### Finite-Dimensional Representations of Yangians in Complex Rank

- MathematicsInternational Mathematics Research Notices
- 2019

We classify the “finite-dimensional” irreducible representations of the Yangians $Y(\mathfrak{g}\mathfrak{l}_t)$ and $Y(\mathfrak{s}\mathfrak{l}_t)$. These are associative ind-algebras in the…

### Indecomposable objects in Khovanov-Sazdanovic's generalizations of Deligne's interpolation categories

- Mathematics
- 2021

Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions and given by quotients of categories of two-dimensional cobordisms. These categories…

## References

SHOWING 1-10 OF 13 REFERENCES

### REPRESENTATION THEORY IN COMPLEX RANK, I

- Mathematics
- 2014

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…

### Representations of Finite Classical Groups: A Hopf Algebra Approach

- Mathematics
- 1981

Structural theory of PSH-algebras.- First applications.- Representations of general linear and affine groups over finite fields.

### Noetherian property of infinite EI categories

- Mathematics
- 2014

It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfying certain…

### Gröbner methods for representations of combinatorial categories

- Mathematics
- 2016

Given a category C of a combinatorial nature, we study the following fundamental question: how does the combinatorial behavior of C affect the algebraic behavior of representations of C? We prove two…

### Deligne categories and reduced Kronecker coefficients

- Mathematics
- 2014

The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups; namely, given three partitions $\lambda, \mu, \tau$ of $n$, the…