# On the Decomposition of Tensor Representations of Symmetric Groups

@article{Nikitin2017OnTD,
title={On the Decomposition of Tensor Representations of Symmetric Groups},
author={Pavel P. Nikitin and Natalia Tsilevich and Anatoly M. Vershik},
journal={Algebras and Representation Theory},
year={2017},
pages={1-14}
}
• Published 2017
• Mathematics
• Algebras and Representation Theory
Following the general idea of Schur–Weyl scheme and using two suitable symmetric groups (instead of one), we define so called decomposition tensor of tensor representations for finite and infinite symmetric group. This makes more explicit the classical problem of decomposing tensor representations of these groups into irreducible components.

#### References

SHOWING 1-10 OF 18 REFERENCES
A Hopf-Algebra Approach to Inner Plethysm
• Mathematics
• 1994
Abstract We use the Hopf algebra structure of the algebra of symmetric functions to study the Adams operators of the complex representation rings of symmetric groups, and we give new proofs of all ofExpand
Schur-Weyl Duality and Representations of Permutation Groups
The Schur-Weyl duality provides a systematic approach to the study of representations of the classical groups. In this contribution we use the Schur-Weyl duality to analyze the naturalExpand
Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras
• Mathematics
• 2010
Preface 1. Representation theory of finite groups 2. The theory of Gelfand-Tsetlin bases 3. The Okounkov-Vershik approach 4. Symmetric functions 5. Content evaluation and character theory 6. TheExpand
A Realization of the Irreducible Representations of Sn Corresponding to 2-Row Diagrams in the Space of Square-Free Symmetric Forms
The article gives a simple realization of the representations of Sn corresponding to 2-row diagrams and an explicit description of the corresponding branching rule. The representations form aExpand
Representation Theory: A First Course
• Mathematics, Computer Science
• 1991
This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representationExpand
Symmetric functions and Hall polynomials
I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functionsExpand
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).
Markov Measures on Young Tableaux and Induced Representations of the Infinite Symmetric Group
• Mathematics
• 2005
We show that the class of so‐called Markov representations of the infinite symmetric group ${\mathfrak G}_{\bf N}$, associated with Markov measures on the space of infinite Young tableaux, coincidesExpand
R T ] 6 M ay 2 00 6 Induced representations of the infinite symmetric group
• 2008
We study the representations of the infinite symmetric group induced from the identity representations of Young subgroups. It turns out that such induced representations can be either of type I or ofExpand
The classical groups : their invariants and representations
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts fromExpand