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3 results

  • Low-degree Hurwitz stacks in the Grothendieck ring

  • Part of
  • Aaron Landesman, Ravi Vakil, Melanie Matchett Wood
  • Journal:
    Compositio Mathematica / Volume 160 / Issue 8 / August 2024
    Published online by Cambridge University Press:
    11 September 2024, pp. 1784-1849
    Print publication:
    August 2024
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  • For $2 \leq d \leq 5$, we show that the class of the Hurwitz space of smooth degree $d$, genus $g$ covers of $\mathbb {P}^1$ stabilizes in the Grothendieck ring of stacks as $g \to \infty$, and we give a formula for the limit. We also verify this stabilization when one imposes ramification conditions on the covers, and obtain a particularly simple answer for this limit when one restricts to simply branched covers.

  • The Representation Ring of the Twisted Quantum Double of a Finite Group

  • S. J. Witherspoon
  • Journal:
    Canadian Journal of Mathematics / Volume 48 / Issue 6 / 01 December 1996
    Published online by Cambridge University Press:
    20 November 2018, pp. 1324-1338
    Print publication:
    01 December 1996
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  • We provide an isomorphism between the Grothendieck ring of modules of the twisted quantum double of a finite group, and a product of centres of twisted group algebras of centralizer subgroups. It follows that this Grothendieck ring is semisimple. Another consequence is a formula for the characters of this ring in terms of representations of twisted group algebras of centralizer subgroups.