Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Some special bases of the 2-swap algebras

Claudio Procesi

Abstract

We study the algebra $Σ_n$ induced by the action of the symmetric group $S_n$ on $V^{\otimes n}$ when $\dim V=2$. Our main result is that the space of symmetric elements of $Σ_n$ is linearly spanned by the involutions of $S_n$.

Some special bases of the 2-swap algebras

Abstract

We study the algebra induced by the action of the symmetric group on when . Our main result is that the space of symmetric elements of is linearly spanned by the involutions of .

Paper Structure

This paper contains 11 sections, 3 theorems, 64 equations.

Table of Contents

  1. Introduction
  2. The algorithm
  3. The computation
  4. The useful relations
  5. Comments
  6. The Formula $\dim \Sigma_n=C_n$
  7. Several bases
  8. $d\geq3$
  9. Transpositions
  10. Appendix explicit formulas
  11. The corresponding rules of substitution:

Key Result

Theorem 1.2

Theorems & Definitions (8)

  • Definition 1.1
  • Theorem 1.2
  • Remark 1.3
  • Remark 1.4
  • Proposition 2.1
  • Remark 2.3
  • Proposition 3.5
  • proof