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Multiplicities of points on a Schubert variety. (English. Abridged French version) Zbl 0849.14018

Let \(G\) be a semisimple simply connected algebraic group, \(T\) a maximal torus in \(G,W\) its Weyl group, and \(B \supset T\) a Borel subgroup. For any \(w \in W\) let \(e_w\) be the point of \(G/B\) and \(X(W)\) the Schubert variety associated to \(W\). Let \(\tau \leq w\) in \(W\), where \(\leq\) is the Bruhat order. In this note the author gives a recursive formula for \(m_\tau (w)\), the multiplicity of \(X(W)\) in \(e_w\). Complete proofs will appear in the author’s forthcoming paper “Tangent cones at singular points on a Schubert variety”.

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
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