Abstract
We give a basis of bideterminants for the coordinate ring K[O(n)] of the orthogonal group O(n,K), where K is an infinite field of characteristic not 2. The bideterminants are indexed by pairs of Young tableaux which are O(n)-standard in the sense of King–Welsh. We also give an explicit filtration of K[O(n)] as an O(n,K)-bimodule, whose factors are isomorphic to the tensor product of orthogonal analogs of left and right Schur modules.
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