Abstract
The “Protean” (see [B. Sagan]) Schur functions reappear (again!) as normalized Grassmann coordinates of a subspace S n −1 of ℙ N n-secant of a rational normal curve ℜ tN , N ≥ n. This property enables a new geometric reformulation of the theory of symmetric functions.
This paper was partially supported by a DCICYT grant and a “del Amo” fellowship of UCM. I met at the IHP in Paris Lascoux, Tyurin and Zak where I discussed a first draft of the paper. The final version was written in Berkeley where I enjoyed Stanley’s combinatorial approach to symmetric functions. Sagan’s criticism on the presentation was so convincing that I tried to imitate this style in [S]. I am grateful to all of them. The LaTeX adaptation of original Gaeta’s manuscript is due to Jorge Caravantes and Laureano Gonzalez-Vega. This is an extended version of what appears in Gaeta’s preprint [G2].
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Gaeta, F. (2010). Symmetric Functions and Secant Spaces of Rational Normal Curves. In: Alonso, M.E., Arrondo, E., Mallavibarrena, R., Sols, I. (eds) Liaison, Schottky Problem and Invariant Theory. Progress in Mathematics, vol 280. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0201-3_15
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