Umbral moonshine

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imported>Pythagoras0님의 2013년 8월 5일 (월) 02:03 판
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introduction

  • $k\in \{1,2,3,4,6,8\}$ or $\ell=k+1\in \{2,3,4,5,7,9\}$

$$ \frac{24}{\ell-1}-1\in \{23,11,7,5,3,2\} $$

  • properties
    • primes dividing $|M_{24}|$
    • $(p+1)|24$
    • $\rm{PSL}(2,\mathbb{F}_p)\subset M_{24}$
  • Mathieu moonshine corresponds to $k=1$ case


Jacobi form


$\mathcal{N}=4$ super conformal algebra

  • $c=6k$, $k\in \mathbb{Z}_{\geq 1}$
  • two types of representations : BPS and non-BPS


extremal Jacobi forms

mock modular form

umbral forms

umbral groups

umbral moonshine conjecture

related items


computational resource


expositions