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The classification of the stable factor-representations of the infinite hyperoctahedral group

N. I. Nessonov

Abstract

The full description of the stable factor-representations of the infinite hyperoctahedral group up to quasi-equivalence obtained.

The classification of the stable factor-representations of the infinite hyperoctahedral group

Abstract

The full description of the stable factor-representations of the infinite hyperoctahedral group up to quasi-equivalence obtained.
Paper Structure (21 sections, 54 theorems, 211 equations)

This paper contains 21 sections, 54 theorems, 211 equations.

Table of Contents

  1. Introduction
  2. Finite type factor-representation of the infinite hyper-octahedral group.
  3. The stable representations of $\mathfrak{S}_\infty$.
  4. The examples
  5. Stable representations induced from the representations of the finite type.
  6. Irreducible representations of $B_n$.
  7. The representations of $B_\infty^{(n)}$ of the finite type.
  8. The results
  9. The properties of the representations ${\rm Ind}^B_{B_\infty^{(n)}}\,^n\!\pi$.
  10. The proof of theorem \ref{['II_1_theorem']}.
  11. The type of representation $\Pi={\rm Ind}^B_{B_\infty^{(n)}}\,^n\!\pi$ in the case $\gamma_0+\gamma_1>0$.
  12. The case $\gamma_0=\gamma_1=0$.
  13. The properties of the stable representations
  14. The standard realisation of $\pi$ and the corresponding representation of the inner automorphism group of $B$.
  15. Quasi-equivalence of the induced representations.
  16. ...and 6 more sections

Key Result

Proposition 3

Let $f$ be a positive functional on $\mathbf{C}^*[G]$ and let $\pi_f$ be the corresponding GNS-representation. If $f$ is stable then $\pi_f$ is stable too.

Theorems & Definitions (92)

  • Definition 1
  • Definition 2: Ver-Nes
  • Proposition 3
  • Definition 4
  • Definition 5
  • Definition 6: TAKES1
  • Proposition 7
  • Corollary 8
  • Proposition 9
  • Theorem 10
  • ...and 82 more