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In the lecture notes Grassmannians: the first example of a moduli space. MIT Open Course Ware. page 7: enter image description here

Are there any formal publications (books/papers) where I can find the formula?

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    $\begingroup$ I don't know the notations involved (what is a special Schubert cycle?), but I suspect that Fulton's Young tableaux (Chapter 10 particularly) is an introduction into this. $\endgroup$ Commented Aug 22, 2015 at 1:43
  • $\begingroup$ Griffiths and Harris, p. 203. It is also in Fulton and Harris (probably in the appendices). $\endgroup$ Commented Aug 22, 2015 at 2:10
  • $\begingroup$ And Manivel, most likely. $\endgroup$
    – Zach H
    Commented Aug 22, 2015 at 3:49
  • $\begingroup$ @JasonStarr: The word "Schubert" appears only once in Fulton&Harris, and that's in a reference. You might be talking of Fulton? (Or you mean the combinatorial Pieri rule? But that's in many places.) $\endgroup$ Commented Aug 22, 2015 at 12:20
  • $\begingroup$ @darijgrinberg: You are correct. I was remembering the combinatorial Pieri rule (I don't have a copy of Fulton-Harris here; I have a Russian Griffiths-Harris). $\endgroup$ Commented Aug 22, 2015 at 12:42

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Here you have some standard references (quoted in the comments):

  • Hiller, Howard. Geometry of Coxeter groups. Research Notes in Mathematics, 54. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. iv+213 pp. ISBN: 0-273-08517-4 MR0649068 (83h:14045)
  • Fulton, William. Young tableaux. With applications to representation theory and geometry. London Mathematical Society Student Texts, 35. Cambridge University Press, Cambridge, 1997. x+260 pp. ISBN: 0-521-56144-2; 0-521-56724-6 MR1464693 (99f:05119)
  • Manivel, Laurent. Symmetric functions, Schubert polynomials and degeneracy loci. Translated from the 1998 French original by John R. Swallow. SMF/AMS Texts and Monographs, 6. Cours Spécialisés [Specialized Courses], 3. American Mathematical Society, Providence, RI; Société Mathématique de France, Paris, 2001. viii+167 pp. ISBN: 0-8218-2154-7 MR1852463 (2002h:05161)

Let me add another nice reference:

  • Hiller, Howard L. Schubert calculus of a Coxeter group. Enseign. Math. (2) 27 (1981), no. 1-2, 57--84. MR0630960 (82m:14031)

Hiller's paper is freely available online here.

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