A basis of bideterminants for the coordinate ring of the orthogonal group

2008/06/09 by Cliff, Gerald · 2 citations
#20G05 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0806.1538

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 isormorphic to the tensor product of orthogonal analogues of left and right Schur modules.

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