Newton-Okounkov bodies for Bott-Samelson varieties and string polytopes for generalized Demazure modules

JOURNAL OF ALGEBRA

卷:515

Article

Fujita, Naoki¹ 

[1] Tokyo Inst Technol, Dept Math, Meguro Ku, 2-12-1 Oh Okayama, Tokyo 1528551, Japan

关键词: Newton-Okounkov body;    Bott-Samelson variety;    String polytope;    Generalized Demazure crystal;   

DOI  :  10.1016/j.jalgebra.2018.08.019

来源: Elsevier

【 摘 要 】

A Newton-Okounkov body is a convex body constructed from a projective variety with a valuation on its homogeneous coordinate ring; this generalizes a Newton polytope for a toric variety. This convex body inherits information about algebraic, geometric, and combinatorial properties of the original projective variety; for instance, Kaveh showed that string polytopes in the representation theory of algebraic groups are examples of Newton-Okounkov bodies for Schubert varieties. In this paper, we extend the notion of string polytopes for Demazure modules to generalized Demazure modules, and prove that the resulting generalized string polytopes are identical to the Newton Okounkov bodies for Bott Samelson varieties with respect to a specific valuation. As an application of this result, we show that these are indeed polytopes. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free