Arthur packets for G2_s Orbits for the dual group: connected split real group with Lie algebra 'g2(R)' complex nilpotent orbits for inner class Complex reductive group of type G2, with involution defining inner class of type 'c', with 2 real forms and 2 dual real forms root datum of inner class: simply connected adjoint root datum of Lie type 'G2' i: orbit number H: semisimple element BC Levi: Bala-Carter Levi Cent_0: identity component of Cent(SL(2)) Z(Cent^0): order of center of derived group of id. comp. of Centralizer C_2: conjugacy classes in Cent(SL(2))_0 with square 1 A(O): orders of conj. classes in component group of centralizer of O #RF: number of real forms of O for all real forms (of integrality datum) in inner class #AP: number of Arthur parameters for O i diagram dim BC Levi Cent_0 Z C_2 A(O) #RF #AP Cent(O) #reps 0 [0,0] 0 2T1 G2 1 2 [1] [1,1] 2 G2 2*=1+1 1 [1,0] 6 A1+T1 A1 2 2 [1] [0,2] 2 SL(2) 2=1+1 2 [0,1] 8 A1+T1 A1 2 2 [1] [0,2] 2 SL(2) 2=1+1 3 [2,0] 10 G2 e 1 1 [1,2,3] [0,2] 2 S3 5*=2+3 4 [2,2] 12 G2 e 1 1 [1] [0,1] 1 G2 1*=1