## 16 Citations

### 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…

### NEW REALIZATIONS OF DEFORMED DOUBLE CURRENT ALGEBRAS AND DELIGNE CATEGORIES

- MathematicsTransformation Groups
- 2022

In this paper, we propose an alternative construction of a certain class of Deformed Double Current Algebras. We construct them as spherical subalgebras of symplectic reection algebras in the Deligne…

### Embedding Deligne's category $\mathrm{Rep}(S_t)$ in the Heisenberg category.

- Mathematics
- 2019

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category $\mathrm{Rep}(S_t)$, to the Heisenberg category. We show that the induced map on…

### Embedding Deligne's category $\mathrm{\Underline{Re}p}(S_t)$ in the Heisenberg category

- MathematicsQuantum Topology
- 2021

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…

### 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…

### Representation theory in non-integral rank (Topics in Combinatorial Representation Theory)

- Mathematics
- 2012

Families of tensor categories, indexed by a continuous parameter $t\in \mathbb{C}$ , which cannot be realized as representation categories of any groups but interpolate usual representation category of these groups in some sense are introduced.

### ON THE PARTITION APPROACH TO SCHUR-WEYL DUALITY AND FREE QUANTUM GROUPS

- Mathematics
- 2014

We give a general definition of classical and quantum groups whose representation theory is “determined by partitions” and study their structure. This encompasses many examples of classical groups…

### ON THE PARTITION APPROACH TO SCHUR-WEYL DUALITY AND FREE QUANTUM GROUPS

- MathematicsTransformation Groups
- 2016

We give a general definition of classical and quantum groups whose representation theory is “determined by partitions” and study their structure. This encompasses many examples of classical groups…

## References

SHOWING 1-10 OF 19 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…

### Finite quantum groupoids and inclusions of finite type

- Mathematics
- 2000

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

- Mathematics
- 2008

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

- Mathematics
- 2008

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

- Mathematics
- 1994

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

- Mathematics
- 2007

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).