The odd case is simpler, there is only one complex spin representation "S", and hermitian structures do not occur. Apart from the trivial case "n" = 1, "S" is always even-dimensional, say dim "S" = 2"N". The real forms of so(2"N",C) are so("K","L") with "K" + "L" = 2"N" and so∗("N",H), while the real forms of sp(2"N",C) are sp(2"N",R) and sp("K","L") with "K" + "L" = "N". The presence of a Clifford action of "V" on "S" forces "K" = "L" in both cases unless "pq" = 0, in which case "KL"=0, which is denoted simply so(2"N") or sp("N"). Hence the odd spin representations may be summarized in the following table.