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On Decomposition Numbers of Diagram Algebras

In: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Author

Listed:
  • Armin Shalile

    (University of Stuttgart, Institute for Algebra and Number Theory)

Abstract

In this paper, we survey an algorithm which determines the decomposition numbers of the partition algebra, Brauer algebra and walled Brauer algebra over a field of characteristic 0. The algorithm is based on the action of a set of distinguished elements of the algebra, the so-called Jucys-Murphy elements. We also outline the proof which is remarkably uniform.

Suggested Citation

  • Armin Shalile, 2017. "On Decomposition Numbers of Diagram Algebras," Springer Books, in: Gebhard Böckle & Wolfram Decker & Gunter Malle (ed.), Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, pages 587-609, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-70566-8_26
    DOI: 10.1007/978-3-319-70566-8_26
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