Advanced Studies in Pure Mathematics

Schubert calculus and puzzles

Allen Knutson

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These are notes for four lectures given at the Osaka summer school on Schubert calculus in 2012, presenting the geometry from the unpublished arXiv:1008.4302 giving an extension of the puzzle rule for Schubert calculus to equivariant $K$-theory, while eliding some of the combinatorial detail. In particular, §3 includes background material on equivariant cohomology and $K$-theory.

Since that school, I have extended the results to arbitrary interval positroid varieties (not just those arising in Vakil's geometric Littlewood-Richardson rule), in the preprint [Kn2].

Article information

Schubert Calculus — Osaka 2012, H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki, eds. (Tokyo: Mathematical Society of Japan, 2016), 185-209

Received: 23 August 2013
Revised: 1 October 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538623000

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Knutson, Allen. Schubert calculus and puzzles. Schubert Calculus — Osaka 2012, 185--209, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/07110185.

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