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Grossberg-Karshon twisted cubes and connected walks
[The 5th Korea Toric Topology Winter Workshop]
Date: 2019-01-23
Speaker : Eunjeong Lee (IBS-CGP)
Abstract : Let G be a complex semisimple simply connected algebraic group of rank r. Let i = (i1; i2; : : : ; in) 2 [r]n be a word decomposition, and let ` = (`1; : : : ; `n) be a sequence of non-negative integers. Grossberg and Karshon introduced a virtual lattice polytope associated to i and `, called a twisted cube, whose lattice points encode characters of representations of B. More precisely, counted lattice points in twisted cube with sign according to a density function, one get the character of the generalized Demazure module associated to i and `. We introduce the notion of hesitant connected `- walks and then prove that the associated Grossberg{Karshon twisted cube is a closed convex polytope precisely when i is a hesitant-connected-`-walkavoiding.
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