caa a22 4500 606160752 CHVBK 20210128100631.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10468-015-9548-5 doi (NATIONALLICENCE)springer-10.1007/s10468-015-9548-5 Minuscule Schubert Varieties: Poset Polytopes, PBW-Degenerated Demazure Modules, and Kogan Faces [Elektronische Daten] [Rekha Biswal, Ghislain Fourier] We study a family of posets and the associated chain and order polytopes. We identify the order polytope as a maximal Kogan face in a Gelfand-Tsetlin polytope of a multiple of a fundamental weight. We show that the character of such a Kogan face equals to the character of a Demazure module which occurs in the irreducible representation of 𝔰 𝔩 n + 1 $\mathfrak {sl}_{n+1}$ having highest weight multiple of fundamental weight and for any such Demazure module there exists a corresponding poset and associated maximal Kogan face. We prove that the chain polytope parametrizes a monomial basis of the associated PBW-graded Demazure module and further, that the Demazure module is a favourable module, e.g. interesting geometric properties are governed by combinatorics of convex polytopes. Thus, we obtain for any minuscule Schubert variety a flat degeneration into a toric projective variety which is projectively normal and arithmetically Cohen-Macaulay. We provide a necessary and sufficient condition on the Weyl group element such that the toric variety associated to the chain polytope and the toric variety associated to the order polytope are isomorphic. Springer Science+Business Media Dordrecht, 2015 Poset polytopes nationallicence PBW filtration nationallicence Schubert varieties nationallicence Kogan faces nationallicence Biswal Rekha The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, India aut Fourier Ghislain Mathematisches Institut, Universität Bonn, Bonn, Germany aut Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1481-1503 1386-923X 18:6<1481 2015 18 10468 https://doi.org/10.1007/s10468-015-9548-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9548-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Biswal Rekha The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, India aut NATIONALLICENCE 700 1- Fourier Ghislain Mathematisches Institut, Universität Bonn, Bonn, Germany aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1481-1503 1386-923X 18:6<1481 2015 18 10468