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  • CHARACTER STACKS ARE PORC COUNT

  • Part of
  • NICK BRIDGER, MASOUD KAMGARPOUR
  • Journal:
    Journal of the Australian Mathematical Society / Volume 115 / Issue 3 / December 2023
    Published online by Cambridge University Press:
    23 September 2022, pp. 289-310
    Print publication:
    December 2023
    • Article
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  • We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a polynomial on residue classes (PORC). The key ingredients in the proof are Lusztig’s Jordan decomposition of complex characters of finite reductive groups and Deriziotis’s results on their genus numbers. As a consequence of our main theorem, we obtain an expression for the E-polynomial of the character stack.