DIRAC COHOMOLOGY FOR COMPLEX GROUPS 13
λR μ ν Unitary E(ρ) μ
(5/2, 3/2, 1, 1/2) (0, 0, 0, 0) (5, 3, 2, 1) NO (1, 0, 0, 0)
(5/2, 3/2, 1, −1/2) (1, 0, 0, 0) (0, 5, 3, 2) NO (1, 1, 0, 0)
(5/2, −3/2, 1, 1/2) (3, 0, 0, 0) (0, 5, 2, 1) NO (3, 1, 0, 0)
(−5/2, 3/2, 1, 1/2) (5, 0, 0, 0) (0, 3, 2, 1) YES 1
(5/2, −3/2, 1, −1/2) (3, 1, 0, 0) (0, 0, 5, 2) NO (3, 1, 1, 1)
(−5/2, 3/2, 1, −1/2) (5, 1, 0, 0) (0, 0, 3, 2) NO (5, 1, 1, 1)
(−5/2, −3/2, 1, 1/2) (5, 3, 0, 0) (0, 0, 2, 1) YES 1
(−5/2, −3/2, 1, −1/2) (5, 3, 1, 0) (0, 0, 0, 2) NO (5, 3, 1, 1)
(5/2, 1/2, 1, 3/2) (1, 1, 0, 0) (2, −2, 2, 5) NO (2, 0, 0, 0)
(−5/2, 1/2, 1, 3/2) (5, 1, 1, 0) (0, 2, −2, 2) NO (5, 2, 0, 0)
(3/2, 5/2, 1, 1/2) (1, 1, 0, 0) (4, −4, 2, 1) NO (1, 0, 0, 0)
(3/2, 5/2, 1, −1/2) (1, 1, 1, 0) (4, −4, 0, 2) NO (2, 0, 0, 0)
(1/2, 3/2, 1, 5/2) (2, 2, 0, 0) (3, −3, 2, 3) NO (3, 1, 0, 0)
(1/2, −3/2, 1, 5/2) (3, 2, 2, 0) (0, 3, −3, 2) NO (7/2, 5/2, 1/2, 1/2)
(5/2, −1/2, 1, −3/2) (2, 2, 0, 0) (1, −1, 5, 2) NO (3, 1, 0, 0)
(−5/2, −1/2, 1, −3/2) (5, 2, 2, 0) (0, 1, −1, 2) NO (5, 2, 2, 1)
(−3/2, −5/2, 1, 1/2) (4, 4, 0, 0) (1, −1, 2, 1) NO (9/2, 7/2, 1/2, 1/2)
(−3/2, −5/2, 1, −1/2) (4, 4, 1, 0) (1, −1, 1, 2) NO (4, 4, 1, 1)
(−1/2, −3/2, 1, 5/2) (3, 3, 0, 0) (2, −2, 3, 2) NO (4, 2, 0, 0)
(−1/2, −3/2, 1, −5/2) (3, 3, 3, 0) (2, 0, −2, 2) NO (9/2, 5/2, 3/2, 1/2)
(5/2, 3/2, −1, 1/2) (2, 0, 0, 0) (0, 5, 3, 1) YES 1
(5/2, 3/2, −1, −1/2) (2, 1, 0, 0) (0, 0, 5, 3) NO
(5/2, −3/2, −1, 1/2) (3, 2, 0, 0) (0, 0, 5, 1) NO
(−5/2, 3/2, −1, 1/2) (5, 2, 0, 0) (0, 0, 3, 1) YES 1
(5/2, −3/2, −1, 1/2) (3, 2, 0, 0) (0, 0, 5, 1) NO
(−5/2, 3/2, −1, −1/2) (5, 2, 1, 0) (0, 0, 0, 3) NO
(−5/2, −3/2, −1, 1/2) (5, 3, 2, 0) (0, 0, 0, 1) YES 1
(−5/2, −3/2, −1, −1/2) (5, 3, 2, 1) (0, 0, 0, 0) YES 1
(5/2, 1/2, −1, 3/2) (2, 1, 1, 0) (0, 2, −2, 5) NO
(−5/2, 1/2, −1, 3/2) (5, 2, 1, 1) (0, 0, 2, −2) NO
(3/2, 5/2, −1, 1/2) (2, 1, 1, 0) (0, 4, −4, 1) NO
(3/2, 5/2, −1, −1/2) (2, 1, 1, 1) (0, 4, 0, −4) NO
(1/2, 3/2, −1, 5/2) (2, 2, 2, 0) (0, 3, −3, 3) NO
(1/2, −3/2, −1, 5/2) (3, 2, 2, 2) (0, 3, −3, 0) NO
(5/2, −1/2, −1, −3/2) (2, 2, 2, 0) (1, 0, −1, 5) NO
(−5/2, −1/2, −1, −3/2) (5, 2, 2, 2) (0, 1, 0, −1) YES 1
(−3/2, −5/2, −1, 1/2) (4, 4, 2, 0) (1, −1, 0, 1) YES 1
(−3/2, −5/2, −1, −1/2) (4, 4, 1, 0) (1, −1, 1, 2) YES 1
(−1/2, −3/2, −1, 5/2) (3, 3, 2, 0) (2, −2, 0, 3) NO
(−1/2, −3/2, −1, −5/2) (3, 3, 3, 2) (2, 0, −2, 0) YES 1
Table 1. Hermitian parameters at ρ/2 for F4.
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