A Basis of Bideterminants for the Coordinate Ring of the Orthogonal Group

We give a basis of bideterminants for the coordinate ring KO(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 KO(n)] as an O(n,K)-bimodule, whose factors are isomorphic to the tensor product of orthogonal analogs of left and right Schur modules.