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- Tags: - #todo/untagged - Refs: - #todo/add-references - Links: - ADE classification - simply laced - loop algebra - Heisenberg algebra - Fock space

SL2

• Subgroups \(G\subseteq {\operatorname{SL}}_2({\mathbf{C}})\) are conjugate to subgroups of \({\operatorname{SU}}_2({\mathbf{C}})\).
• There is a one-to-one correspondence between non-trivial finite subgroups \(G\) of \(S U(2)\) and the Dynkin diagrams \(Q\) of types containing no double or triple edges:
  • \(A_{n}(n \geq 1)\),
  • \(D_{n}(n \geq 4)\),
  • \(E_{6}\),
  • \(E_{7}\),\
  • \(E_{8}\)