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Poset polytopes and pipe dreams: types C and B

Published 25 Feb 2024 in math.RT, math.AG, and math.CO | (2402.16207v2)

Abstract: The first part of this paper concerns type C. We present new explicitly defined families of algebro-combinatorial structures of three kinds: combinatorial bases in representations, Newton--Okounkov bodies of flag varieties and toric degenerations of flag varieties. All three families are parametrized by the same family of polytopes: the marked chain-order polytopes of Fang and Fourier which interpolate between the type C Gelfand--Tsetlin and FFLV polytopes. Thus, in each case the obtained structures interpolate between the well-known bases, Newton--Okounkov bodies or degenerations associated with the latter two polytopes. We then obtain similar results for type B after introducing a new family of poset polytopes to be considered in place of marked chain-order polytopes. In both types our constructions and proofs rely crucially on a combinatorial connection between poset polytopes and pipe dreams.

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