相关论文: On the partition approach to Schur-Weyl duality an…

We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…

In this thesis we will study matrix models with discrete gauge group $S_N$. We will put these matrix models into a generalized Schur-Weyl duality framework where dual algebras, known as partition algebras, emerge. These form generalizations…

There is a classical connection between the representation theory of the symmetric group and the general linear group called Schur-Weyl duality. Variations on this principle yield analogous connections between the symmetric group and other…

Within the framework of unitary easy quantum groups, we study an analogue of Brauer's Schur-Weyl approach to the representation theory of the orthogonal group. We consider concrete combinatorial categories whose morphisms are formed by…

Let $V$ be a free module of rank $n$ over a commutative unital ring $k$. We prove that tensor space $V^{\otimes r}$ satisfies Schur--Weyl duality, regarded as a bimodule for the action of the group algebra of the Weyl group of…

Schur-Weyl duality is a fundamental framework in combinatorial representation theory. It intimately relates the irreducible representations of a group to the irreducible representations of its centralizer algebra. We investigate the analog…

Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into…

We propose a definition of partition quantum spaces. They are given by universal $C^*$-algebras whose relations come from partitions of sets. We ask for the maximal compact matrix quantum group acting on them. We show how those fit into the…

We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those of other affine diagram algebras. In particular we show that it extends the Schur-Weyl…

Compact matrix quantum groups are strongly determined by their intertwiner spaces, due to a result by S.L. Woronowicz. In the case of easy quantum groups, the intertwiner spaces are given by the combinatorics of partitions, see the inital…

This thesis investigates quantum cloning and related quantum entanglement problems using core concepts of representation theory, in particular those associated with the symmetric group. The research explores Schur-Weyl duality and its…

The classical Peter-Weyl theorem describes the structure of the space of functions on a semi-simple algebraic group. On the level of characters (in type A) this boils down to the Cauchy identity for the products of Schur polynomials. We…

We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n, and give a complete reducibility result. These quantum groups have a…

We generalize categories of spatial partitions in the sense of C\'ebron-Weber by introducing new base partitions. This allows us to construct additional examples of free orthogonal quantum groups but yields the same class of spatial…

The twin group $TW_n$ on $n$ strands is the group generated by $t_1, \dots, t_{n-1}$ with defining relations $t_i^2=1$, $t_it_j = t_jt_i$ if $|i-j|>1$. We find a new instance of semisimple Schur--Weyl duality for tensor powers of a natural…

The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…

The classical case of Schur--Weyl duality states that the actions of the group algebras of $GL_n$ and $S_d$ on the $d^{th}$-tensor power of a free module of finite rank centralize each other. We show that Schur--Weyl duality holds for…

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the…

We define the notion of a (linearly reductive) center for a linearly reductive quantum group, and show that the quotient of a such a quantum group by its center is simple whenever its fusion semiring is free in the sense of Banica and…

The integral formulae pertaining to the unitary group $\mathsf{U}(d)$ have been comprehensively reviewed, yielding fresh results and innovative proofs. Central to the derivation of these formulae lies the employment of Schur-Weyl duality, a…