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Lee, Eun Jeong
기하학 수리물리 연구단
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Grossberg-Karshon twisted cubes and hesitant jumping walk avoidance

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Title
Grossberg-Karshon twisted cubes and hesitant jumping walk avoidance
Author(s)
Eunjeong Lee
Subject
BOTT-SAMELSON VARIETIES, ; NEWTON-OKOUNKOV BODIES
Publication Date
2020-08
Journal
ELECTRONIC JOURNAL OF COMBINATORICS, v.27, no.3, pp.3.34
Publisher
ELECTRONIC JOURNAL OF COMBINATORICS
Abstract
ⓒ The author. Let G be a complex simply-laced semisimple algebraic group of rank r and B a Borel subgroup. Let i is an element of [r](n) be a word and let l = (l(1), ...,l(n)) be a sequence of non-negative integers. Grossberg and Karshon introduced a virtual lattice polytope associated to i and l called a twisted cube, whose lattice points encode the character of a B-representation. More precisely, lattice points in the twisted cube, counted with sign according to a certain density function, yield the character of the generalized Dernazure module determined by i and l. In a recent work, the author and Harada described precisely when the Grossberg-Karshon twisted cube is untwisted, i.e., the twisted cube is a closed convex polytope, in the situation when the integer sequence l comes from a weight lambda for G. However, not every integer sequence l comes from a weight for G. In the present paper, we interpret the untwistedness of Grossberg Karshon twisted cubes associated with any word i and any integer sequence t using the combinatorics of i and l. Indeed, we prove that the Grossberg-Karshon twisted cube is untwisted precisely when i is hesitant-jumping-l-walk-avoiding
URI
https://pr.ibs.re.kr/handle/8788114/7693
DOI
10.37236/9278
ISSN
1077-8926
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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