2015/04/18 by Megumi Harada, Jihyeon Jessie Yang · 17 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Character (mathematics) #Combinatorics #Geometry #Lattice (music) #Mathematics #Physics #Polytope #Pure mathematics #Statistics #Valuation (finance) #Variety (cybernetics) #math.AG #math.RT
paper · pdf · doi:10.1307/mmj/1465329020
published in The Michigan Mathematical Journal 65(2) (Institute of Mathematical Statistics) · 17 pages, 3 figures. References added
arxiv created 2015/04/18 · openalex publication_date 2016/06/01 · openalex created_date 2016/06/24 · arxiv updated 2018/06/20 · openalex updated_date 2026/08/05
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. In particular, the Grossberg-Karshon twisted cubes that appear in the present manuscript are in fact untwisted (though possibly degenerate).