Geometric mitosis and Newton-Okounkov polytopes

P. 1484–1487.

Valentina Kiritchenko

In [K], a convex-geometric algorithm was introduced for building new analogs of Gelfand–Zetlin polytopes for arbitrary reductive groups. Conjecturally, these polytopes coincide with the Newton–Okounkov polytopes of flag varieties for a geometric valuation. I outline an algorithm (geometric mitosis) for finding collec- tion of faces in these polytopes that represent a given Schubert cycle. For GL_n and Gelfand–Zetlin polytopes, this algorithm reduces to a geometric version of Knutson–Miller mitosis introduced in [KST].

Ключевые слова: исчисление Шуберта, Schubert calculus, Newton-Okounkov polytopes, многогранники Ньютона-Окунькова

В книге

Oberwolfach Reports

Vol. 11. Issue 2. , Zürich: European Mathematical Society Publishing house, 2014.