Newton-Okounkov bodies of Bott-Samelson varieties and Grossberg-Karshon twisted cubes

Abstract

We describe, under certain conditions, the Newton-Okounkov body of a Bott-Samelson variety as a lattice polytope defined by an explicit list of inequalities. The valuation that we use to define the Newton-Okounkov body is different from that used previously in the literature. The polytope that arises is a special case of the Grossberg-Karshon twisted cubes studied by Grossberg and Karshon in connection to character formulae for irreducible $G$-representations and also studied previously by the authors in relation to certain toric varieties associated to Bott-Samelson varieties.

17 pages, 3 figures. References added

References in corpus (2)

• Convex bodies and algebraic equations on affine varieties
• Newton-Okounkov bodies for Bott-Samelson varieties and string polytopes for generalized Demazure modules

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