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Zbl 0727.13005
Sturmfels, Bernd; White, Neil
Stanley decompositions of the bracket ring. (English)
[J] Math. Scand. 67, No.2, 183-189 (1990). ISSN 0025-5521

We give an explicit Stanley decomposition of the bracket ring ${\bbfB}\sb{n,d}$, that is, the commutative ring generated by the $d\times d$-minors of a generic $n\times d$-matrix. A Stanley decomposition is a direct sum decomposition of the additive group of the ring, each summand of which is a bracket monomial times a subring generated freely by brackets. The decomposition is obtained via a shelling of the simplicial complex determined by the standard tableaux. Our construction has important applications in the Cushman-Sanders normal form theory for nilpotent vector fields.
[N.White (Gainesville)]

MSC 2000:: *13C40 Linkage, complete intersections and determinantal ideals
13F20 Polynomial rings
14M12 Determinantal varieties

Keywords: Stanley decomposition; bracket ring; shelling of the simplicial complex; standard tableaux; nilpotent vector fields

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