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On the quantum flag manifold \({{SU}_{q}} (3)/{\mathbb{T}^2}\)

  • Tomasz Brzeziński
  • Wojciech Szymański
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The structure of the C*-algebra of functions on the quantum flag manifold \( {{SU}_{q}} (3)/ {\mathbb{T}^2}\) is investigated. Building on the representation theory of \( C({SU_q}(3)) \), we analyze irreducible representations and the primitive ideal space of \( C({SU_q}(3)/\mathbb{T}^2) \), with a view towards unearthing the “quantum sphere bundle” \( \mathbb{C}{{P}^1_q} \rightarrow {SU_q}(3)/\mathbb{T}^2 \rightarrow \mathbb{C}{{P}^2_q}\) .

Keywords

Quantum flag manifold quantum fibre bundle quantum SU(3) group. 

Mathematics Subject Classification (2000)

46L65 81R60. 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tomasz Brzeziński
    • 1
    • 2
    • 3
  • Wojciech Szymański
    • 2
  1. 1.Department of MathematicsSwansea University Swansea University Bay Campus Fabian WaySwanseaUK
  2. 2.Department of MathematicsUniversity of Białystok K. Ciołkowskiego 1MBiałystokPoland
  3. 3.Department of Mathematics and Computer ScienceUniversity of Southern Denmark Campusvej 55 5230Odense MDenmark

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